Is there a math expression equivalent to the conditional ternary operator?












42












$begingroup$


Is there a math equivalent of the ternary conditional operator as used in programming?



a = b + (c > 0 ? 1 : 2)


The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.










share|cite|improve this question











$endgroup$








  • 5




    $begingroup$
    @Alex $a = b + 2 - u(c)$
    $endgroup$
    – eyeballfrog
    Mar 5 at 5:45








  • 16




    $begingroup$
    A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
    $endgroup$
    – Winther
    2 days ago








  • 5




    $begingroup$
    In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
    $endgroup$
    – TonyK
    2 days ago








  • 3




    $begingroup$
    Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
    $endgroup$
    – Konrad Rudolph
    2 days ago






  • 1




    $begingroup$
    What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
    $endgroup$
    – a CVn
    2 days ago
















42












$begingroup$


Is there a math equivalent of the ternary conditional operator as used in programming?



a = b + (c > 0 ? 1 : 2)


The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.










share|cite|improve this question











$endgroup$








  • 5




    $begingroup$
    @Alex $a = b + 2 - u(c)$
    $endgroup$
    – eyeballfrog
    Mar 5 at 5:45








  • 16




    $begingroup$
    A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
    $endgroup$
    – Winther
    2 days ago








  • 5




    $begingroup$
    In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
    $endgroup$
    – TonyK
    2 days ago








  • 3




    $begingroup$
    Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
    $endgroup$
    – Konrad Rudolph
    2 days ago






  • 1




    $begingroup$
    What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
    $endgroup$
    – a CVn
    2 days ago














42












42








42


9



$begingroup$


Is there a math equivalent of the ternary conditional operator as used in programming?



a = b + (c > 0 ? 1 : 2)


The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.










share|cite|improve this question











$endgroup$




Is there a math equivalent of the ternary conditional operator as used in programming?



a = b + (c > 0 ? 1 : 2)


The above means that if $c$ is greater than $0$ then $a = b + 1$, otherwise $a = b + 2$.







notation computer-science






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 29 mins ago









Wharf Rat

999




999










asked Mar 5 at 5:23









dataphiledataphile

348310




348310








  • 5




    $begingroup$
    @Alex $a = b + 2 - u(c)$
    $endgroup$
    – eyeballfrog
    Mar 5 at 5:45








  • 16




    $begingroup$
    A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
    $endgroup$
    – Winther
    2 days ago








  • 5




    $begingroup$
    In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
    $endgroup$
    – TonyK
    2 days ago








  • 3




    $begingroup$
    Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
    $endgroup$
    – Konrad Rudolph
    2 days ago






  • 1




    $begingroup$
    What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
    $endgroup$
    – a CVn
    2 days ago














  • 5




    $begingroup$
    @Alex $a = b + 2 - u(c)$
    $endgroup$
    – eyeballfrog
    Mar 5 at 5:45








  • 16




    $begingroup$
    A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
    $endgroup$
    – Winther
    2 days ago








  • 5




    $begingroup$
    In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
    $endgroup$
    – TonyK
    2 days ago








  • 3




    $begingroup$
    Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
    $endgroup$
    – Konrad Rudolph
    2 days ago






  • 1




    $begingroup$
    What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
    $endgroup$
    – a CVn
    2 days ago








5




5




$begingroup$
@Alex $a = b + 2 - u(c)$
$endgroup$
– eyeballfrog
Mar 5 at 5:45






$begingroup$
@Alex $a = b + 2 - u(c)$
$endgroup$
– eyeballfrog
Mar 5 at 5:45






16




16




$begingroup$
A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
$endgroup$
– Winther
2 days ago






$begingroup$
A better question here is: what is good notation in this case. There are many ways of writing this, many ways which one would almost never use (like the accepted answer).
$endgroup$
– Winther
2 days ago






5




5




$begingroup$
In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
$endgroup$
– TonyK
2 days ago






$begingroup$
In C-derived languages at least, you have made a grievous error! Your expression parses as a = (b + c) > 0 ? 1 : 2. I always use parentheses in these cases, even when they are not strictly necessary.
$endgroup$
– TonyK
2 days ago






3




3




$begingroup$
Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
$endgroup$
– Konrad Rudolph
2 days ago




$begingroup$
Just to clarify, by “ternary operator” you really mean “conditional operator”? Or are interested in any kind of ternary operator, regardless of semantics?
$endgroup$
– Konrad Rudolph
2 days ago




1




1




$begingroup$
What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
$endgroup$
– a CVn
2 days ago




$begingroup$
What @KonradRudolph said; you are showing the conditional operator, which is a ternary (takes three arguments; compare unary and binary) operator. I don't think the C language has any other ternary operator, and some form of the conditional operator is found in many languages because it's very convenient to have, but there's no rule that says a language couldn't include other ternary operators alongside (or without having) a conditional operator.
$endgroup$
– a CVn
2 days ago










11 Answers
11






active

oldest

votes


















59












$begingroup$

From physics, I'm used to seeing the Kronecker delta,$$
{delta}_{ij}
equiv
left{
begin{array}{lll}
1 &text{if} & i=j \
0 &text{else}
end{array}
right. _{,}
$$
and I think people who work with it find the slightly generalized notation$$
{delta}_{left[text{condition}right]}
equiv
left{
begin{array}{lll}
1 &text{if} & left[text{condition}right] \
0 &text{else}
end{array}
right.
$$
to be pretty natural to them.



So, I tend to use $delta_{left[text{condition}right]}$ for a lot of things. Just seems so simple and well-understood.



Transforms:




  1. Basic Kronecker delta:
    To write the basic Kronecker delta in terms of the generalized Kronecker delta, it's just$$
    delta_{ij}
    Rightarrow
    delta_{i=j}
    ,.$$
    It's almost the same notation, and I think most folks can figure it out pretty easily without needing it explained.


  2. Conditional operator:
    The "conditional operator" or "ternary operator" for the simple case of ?1:0:$$
    begin{array}{ccccc}
    boxed{
    begin{array}{l}
    texttt{if}~left(texttt{condition}right) \
    { \
    ~~~~texttt{return 1;} \
    } \
    texttt{else} \
    { \
    ~~~~texttt{return 0;} \
    }
    end{array}
    ~} &
    Rightarrow &
    boxed{~
    texttt{condition ? 1 : 0}
    ~} &
    Rightarrow &
    delta_{i=j}
    end{array}
    _{.}
    $$
    Then if you want a non-zero value for the false-case, you'd just add another Kronecker delta, $delta_{operatorname{NOT}left(left[text{condition}right]right)} ,$ e.g. $delta_{i neq j} .$


  3. Indicator function:
    @SiongThyeGoh's answer recommended using indicator function notation. I'd rewrite their example like$$
    begin{array}{ccccc}
    underbrace{a=b+1+mathbb{1}_{(-infty, 0]}(c)}
    _{text{their example}}
    &
    Rightarrow &
    underbrace{a=b+1+ delta_{c in left(-infty, 0right]}}
    _{text{direct translation}} &
    Rightarrow &
    underbrace{a=b+1+ delta_{c , {small{leq}} , 0}}
    _{text{cleaner form}}
    end{array}
    ,.
    $$


  4. Iverson bracket:
    Iverson bracket notation, as suggested in @FredH's answer, is apparently the same thing; according to Wikipedia, it's meant as a generalization of the Kronecker delta, except they drop the $delta$ entirely, just putting the condition in square-brackets. In a context in readers expect it, Iverson bracket notation might be preferable if conditionals will be used a lot.





Note: "Conditional operator" rather than "ternary operator".



The conditional operator, condition ? trueValue : falseValue, has 3 arguments, making it an example of a ternary operator. By contrast, most other operators in programming tend to be unary operators (which have 1 argument) or binary operators (which have 2 arguments).



Since the conditional operator is fairly unique in being a ternary operator, it's often been called "the ternary operator", leading many to believe that that's its name. However, "conditional operator" is more specific and should generally be preferred.






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
    $endgroup$
    – dataphile
    2 days ago










  • $begingroup$
    @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
    $endgroup$
    – Nat
    2 days ago








  • 2




    $begingroup$
    The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
    $endgroup$
    – Konrad Rudolph
    2 days ago








  • 1




    $begingroup$
    The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
    $endgroup$
    – J.G.
    2 days ago






  • 1




    $begingroup$
    Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
    $endgroup$
    – Nat
    yesterday



















59












$begingroup$

The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly define a function
$$f(b,c)=begin {cases} b+1&c gt 0\
b+2 & c le 0 end {cases}$$



You can also define functions with any number of inputs you want, so you can define $f(a,b,c)=a(b+c^2)$, for example. This is a ternary function.






share|cite|improve this answer











$endgroup$









  • 14




    $begingroup$
    Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
    $endgroup$
    – Džuris
    2 days ago






  • 19




    $begingroup$
    @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
    $endgroup$
    – frabala
    2 days ago






  • 21




    $begingroup$
    Once again, clarity beats compactness when it comes to mathematics.
    $endgroup$
    – Asaf Karagila
    2 days ago






  • 8




    $begingroup$
    Well-chosen compact notations can contribute to clarity rather than detract from it, though.
    $endgroup$
    – Henning Makholm
    2 days ago






  • 7




    $begingroup$
    @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
    $endgroup$
    – Konrad Rudolph
    2 days ago





















40












$begingroup$

In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. Using this notation, you could write
$$
a = b + 2 - [c gt 0].
$$






share|cite|improve this answer











$endgroup$









  • 7




    $begingroup$
    aka en.wikipedia.org/wiki/Iverson_bracket
    $endgroup$
    – qwr
    2 days ago






  • 6




    $begingroup$
    I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
    $endgroup$
    – Rahul
    2 days ago








  • 5




    $begingroup$
    I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
    $endgroup$
    – J. M. is not a mathematician
    2 days ago






  • 4




    $begingroup$
    Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
    $endgroup$
    – pipe
    2 days ago








  • 2




    $begingroup$
    Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
    $endgroup$
    – safkan
    23 hours ago



















24












$begingroup$

Using the indicator function notation:$$a=b+1+mathbb{1}_{(-infty, 0]}(c)$$






share|cite|improve this answer











$endgroup$









  • 1




    $begingroup$
    Indicator is definitely the way to go, since the conditional can define an arbitrary set.
    $endgroup$
    – eyeballfrog
    Mar 5 at 5:47










  • $begingroup$
    Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
    $endgroup$
    – dataphile
    Mar 5 at 5:52






  • 2




    $begingroup$
    I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
    $endgroup$
    – Christopher
    2 days ago








  • 1




    $begingroup$
    The indicator function isn’t a ternary operator, it only has two operands.
    $endgroup$
    – Konrad Rudolph
    2 days ago












  • $begingroup$
    I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
    $endgroup$
    – David Richerby
    18 hours ago



















14












$begingroup$

In math, equations are written in piecewise form by having a curly brace enclose multiple lines; each one with a condition excepting the last which has "otherwise".



There are a few custom operators that also occasionally make an appearance. E.g. the Heavyside function mentioned by Alex, the Dirac function, and the cyclical operator $delta_{ijk}$ - all of which can be used to emulate conditional behaviour.






share|cite|improve this answer









$endgroup$





















    5












    $begingroup$

    One should realize that operators are just a fancy way of using functions.
    So a ternary operator is a function of 3 variables that is notated in a different way. Is that useful? The answer is mostly not. Also realize that any mathematician is allowed to introduce any notation he feels is illustrative.



    Let's review why we use binary operators at all like in a+b*c . Because parameters and results are of the same type, it makes sense to leave out parentheses and introduce complicated priority rules. Imagine that a b c are numbers and we have a normal + and a peculiar * that results in dragons. Now the expression doesn't make sense (assumming a high priority *), because there is no way to add numbers and dragons. Thusly most ternary operators results in a mess.



    With a proper notation there are examples of ternary operations. For example, there is a special notation for "sum for i from a to b of expression". This takes two boundaries (numbers) and a function from a number of that type that results in another number. (Mathematician, read "element of an addition group" for number.)
    The notation for integration is similarly ternary.

    So in short ternary operators exist, and you can define your own. They are in general accompagnied with a special notation, or they are not helpful.



    Now back to the special case you mention.
    Because truth values are implied in math, an expression like "if a then b else c" makes sense if a represens a truth value like (7<12). The above expression is understood in every mathematical context. However in a context where truth values are not considered a set, (if .. then .. else ..) would not be considered an operator/function, but a textual explanation. A general accepted notation could be useful in math, but I'm not aware there is one. That is probably, because like in the above, informal notations are readily understood.






    share|cite|improve this answer









    $endgroup$





















      5












      $begingroup$

      I think mathematicians should not be afraid to use the Iverson bracket, including when teaching, as this is a generally very useful notation whose only slightly unusual feature is to introduce a logical expression in the middle of an algebraic one (but one already regularly finds conditions inside set-theoretic expressions, so it really is not a big deal). It may avoid a lot of clutter, notably many instances of clumsy expressions by cases with a big unmatched brace (which is usually only usable as the right hand side of a definition). Since brackets do have many other uses in mathematics, I personally prefer a typographically distinct representation of Iverson brackets, rendering your example as
      $$def[#1]{[![{#1}]!]}
      a= b + [c>0]1 + [cnot>0]2.
      $$

      This works best in additive context (though one can use Iverson brackets in the exponent for optional multiplicative factors). It is not really ideal for general two-way branches, as the condition must be repeated twice, one of them in negated form, but it happens that most of the time one needs $0$ as the value for one branch anyway.



      As a more concise two-way branch, I can recall that Algol68 introduced the notation $b+(c>0mid 1mid 2)$ for the right-hand side of your equation; though this is a programming language and not mathematics, it was designed by mathematicians. They also had notation for multi-way branching: thus the solution to the recursion $a_{n+2}=a_{n+1}-a_n$ with initial values $a_0=0$, $a_1=1$ can be written
      $$
      a_n=(nbmod 6+1mid 0,1,1,0,-1,-1)
      $$

      (where the "${}+1$" is needed because in 1968 they still counted starting from $1$, which is a mistake), which is reasonably concise and readable, compared to other ways to express this result. Also consider, for month $m$ in year $y$, the number
      $$
      ( m mid 31,(ybmod 4=0land ybmod 100neq0lor ybmod400=0mid 29mid 28)
      ,31,30,31,30,31,31,30,31,30,31).
      $$






      share|cite|improve this answer









      $endgroup$





















        3












        $begingroup$

        The accepted answer from Nat, suggesting the Kronecker Delta, is correct. However, it is also important to note that one of the highly upvoted answers here, which claims the C ternary operator x?y:z is not ternary is incorrect.



        Mathematically, the expression x?y:z can be expressed as a function of three variables:
        $$f(x,y,z)=begin {cases} y&xneq 0\
        z & x=0 end {cases}$$



        Note that in programming an expression such as $a<b$ could be used for $x$. If the expression is true, then $x=1$, otherwise $x=0$.



        About nomenclature: computer programmers have used the phrase the ternary operator to mean exactly this since at least the 1970s. Of course, among mathematicians, it would simply be a ternary operator and we would qualify it by either stating a programming language, e.g., the C ternary operator, or by calling it the conditional operator.






        share|cite|improve this answer










        New contributor




        hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
        Check out our Code of Conduct.






        $endgroup$





















          1












          $begingroup$

          There are many good answers that give notation for, “if this condition holds, then 1, else 0.” This corresponds to an even simpler expression in C;(x>1) is equivalent to (x>1 ? 1 : 0).



          It’s worth noting that the ternary operator is more general than that. If the arguments are elements of a ring, you could express c ? a : b with (using Iverson-bracket notation) $(a-b) cdot [c] + b$, but not otherwise. (And compilers frequently use this trick, in a Boolean ring, to compile conditionals without needing to execute a branch instruction.) In a C program, evaluating the expressions $a$ or $b$ might have side-effects, such as deleting a file or printing a message to the screen. In a mathematical function, this isn’t something you would worry about, and a programming language where this is impossible is called functional.



          Ross Millikan gave the most standard notation, a cases block. The closest equivalent in mathematical computer science is the if-then-else function of Lambda Calculus.






          share|cite|improve this answer











          $endgroup$













          • $begingroup$
            "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
            $endgroup$
            – a CVn
            2 days ago






          • 1




            $begingroup$
            @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
            $endgroup$
            – Davislor
            2 days ago












          • $begingroup$
            @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
            $endgroup$
            – Davislor
            2 days ago



















          1












          $begingroup$

          Following solution is not defined for $c = 0$; however it uses very basic operations only, which might be useful as you probably look for an expression to implement in a program:



          $$a = b + 1lambda + 2(1-lambda)$$



          where



          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$





          You need to make the problem discrete and make a choice from two values. So, given some value $c in mathbb{R}$ we need to calculate some value $lambda in {0,1}$ depnding on $c<0$ or $c>0$.



          Knowing that



          $$frac{|c|}{c} in {1,-1}$$



          we can calculate the $lambda$ as follows:



          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$



          Now that our $lambda in {0,1}$ we can do the "choice" between the two constants $d$ and $e$ as follows:



          $$dlambda + e(1-lambda)$$



          which equals $d$ for $lambda = 1$, and $e$ for $lambda = 0$.






          share|cite|improve this answer










          New contributor




          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
          Check out our Code of Conduct.






          $endgroup$













          • $begingroup$
            And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
            $endgroup$
            – David Richerby
            18 hours ago



















          0












          $begingroup$

          Fundamentally, the non-answer is the answer. Whatever notation you think you might want to use to express "$a=b+1$ if $c>0$ and $a=b+2$ otherwise" or
          $$a=begin{cases}b+1 &text{if }c>0\b+2 &text{otherwise}end{cases}$$
          is much harder to read than either of those two things.






          share|cite|improve this answer









          $endgroup$













          • $begingroup$
            The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
            $endgroup$
            – dataphile
            16 hours ago






          • 1




            $begingroup$
            Most of any mathematics paper is natural language. There's a reason for that.
            $endgroup$
            – David Richerby
            15 hours ago











          Your Answer





          StackExchange.ifUsing("editor", function () {
          return StackExchange.using("mathjaxEditing", function () {
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          });
          });
          }, "mathjax-editing");

          StackExchange.ready(function() {
          var channelOptions = {
          tags: "".split(" "),
          id: "69"
          };
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function() {
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled) {
          StackExchange.using("snippets", function() {
          createEditor();
          });
          }
          else {
          createEditor();
          }
          });

          function createEditor() {
          StackExchange.prepareEditor({
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader: {
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          },
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          });


          }
          });














          draft saved

          draft discarded


















          StackExchange.ready(
          function () {
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3135798%2fis-there-a-math-expression-equivalent-to-the-conditional-ternary-operator%23new-answer', 'question_page');
          }
          );

          Post as a guest















          Required, but never shown

























          11 Answers
          11






          active

          oldest

          votes








          11 Answers
          11






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes









          59












          $begingroup$

          From physics, I'm used to seeing the Kronecker delta,$$
          {delta}_{ij}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & i=j \
          0 &text{else}
          end{array}
          right. _{,}
          $$
          and I think people who work with it find the slightly generalized notation$$
          {delta}_{left[text{condition}right]}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & left[text{condition}right] \
          0 &text{else}
          end{array}
          right.
          $$
          to be pretty natural to them.



          So, I tend to use $delta_{left[text{condition}right]}$ for a lot of things. Just seems so simple and well-understood.



          Transforms:




          1. Basic Kronecker delta:
            To write the basic Kronecker delta in terms of the generalized Kronecker delta, it's just$$
            delta_{ij}
            Rightarrow
            delta_{i=j}
            ,.$$
            It's almost the same notation, and I think most folks can figure it out pretty easily without needing it explained.


          2. Conditional operator:
            The "conditional operator" or "ternary operator" for the simple case of ?1:0:$$
            begin{array}{ccccc}
            boxed{
            begin{array}{l}
            texttt{if}~left(texttt{condition}right) \
            { \
            ~~~~texttt{return 1;} \
            } \
            texttt{else} \
            { \
            ~~~~texttt{return 0;} \
            }
            end{array}
            ~} &
            Rightarrow &
            boxed{~
            texttt{condition ? 1 : 0}
            ~} &
            Rightarrow &
            delta_{i=j}
            end{array}
            _{.}
            $$
            Then if you want a non-zero value for the false-case, you'd just add another Kronecker delta, $delta_{operatorname{NOT}left(left[text{condition}right]right)} ,$ e.g. $delta_{i neq j} .$


          3. Indicator function:
            @SiongThyeGoh's answer recommended using indicator function notation. I'd rewrite their example like$$
            begin{array}{ccccc}
            underbrace{a=b+1+mathbb{1}_{(-infty, 0]}(c)}
            _{text{their example}}
            &
            Rightarrow &
            underbrace{a=b+1+ delta_{c in left(-infty, 0right]}}
            _{text{direct translation}} &
            Rightarrow &
            underbrace{a=b+1+ delta_{c , {small{leq}} , 0}}
            _{text{cleaner form}}
            end{array}
            ,.
            $$


          4. Iverson bracket:
            Iverson bracket notation, as suggested in @FredH's answer, is apparently the same thing; according to Wikipedia, it's meant as a generalization of the Kronecker delta, except they drop the $delta$ entirely, just putting the condition in square-brackets. In a context in readers expect it, Iverson bracket notation might be preferable if conditionals will be used a lot.





          Note: "Conditional operator" rather than "ternary operator".



          The conditional operator, condition ? trueValue : falseValue, has 3 arguments, making it an example of a ternary operator. By contrast, most other operators in programming tend to be unary operators (which have 1 argument) or binary operators (which have 2 arguments).



          Since the conditional operator is fairly unique in being a ternary operator, it's often been called "the ternary operator", leading many to believe that that's its name. However, "conditional operator" is more specific and should generally be preferred.






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
            $endgroup$
            – dataphile
            2 days ago










          • $begingroup$
            @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
            $endgroup$
            – Nat
            2 days ago








          • 2




            $begingroup$
            The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago








          • 1




            $begingroup$
            The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
            $endgroup$
            – J.G.
            2 days ago






          • 1




            $begingroup$
            Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
            $endgroup$
            – Nat
            yesterday
















          59












          $begingroup$

          From physics, I'm used to seeing the Kronecker delta,$$
          {delta}_{ij}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & i=j \
          0 &text{else}
          end{array}
          right. _{,}
          $$
          and I think people who work with it find the slightly generalized notation$$
          {delta}_{left[text{condition}right]}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & left[text{condition}right] \
          0 &text{else}
          end{array}
          right.
          $$
          to be pretty natural to them.



          So, I tend to use $delta_{left[text{condition}right]}$ for a lot of things. Just seems so simple and well-understood.



          Transforms:




          1. Basic Kronecker delta:
            To write the basic Kronecker delta in terms of the generalized Kronecker delta, it's just$$
            delta_{ij}
            Rightarrow
            delta_{i=j}
            ,.$$
            It's almost the same notation, and I think most folks can figure it out pretty easily without needing it explained.


          2. Conditional operator:
            The "conditional operator" or "ternary operator" for the simple case of ?1:0:$$
            begin{array}{ccccc}
            boxed{
            begin{array}{l}
            texttt{if}~left(texttt{condition}right) \
            { \
            ~~~~texttt{return 1;} \
            } \
            texttt{else} \
            { \
            ~~~~texttt{return 0;} \
            }
            end{array}
            ~} &
            Rightarrow &
            boxed{~
            texttt{condition ? 1 : 0}
            ~} &
            Rightarrow &
            delta_{i=j}
            end{array}
            _{.}
            $$
            Then if you want a non-zero value for the false-case, you'd just add another Kronecker delta, $delta_{operatorname{NOT}left(left[text{condition}right]right)} ,$ e.g. $delta_{i neq j} .$


          3. Indicator function:
            @SiongThyeGoh's answer recommended using indicator function notation. I'd rewrite their example like$$
            begin{array}{ccccc}
            underbrace{a=b+1+mathbb{1}_{(-infty, 0]}(c)}
            _{text{their example}}
            &
            Rightarrow &
            underbrace{a=b+1+ delta_{c in left(-infty, 0right]}}
            _{text{direct translation}} &
            Rightarrow &
            underbrace{a=b+1+ delta_{c , {small{leq}} , 0}}
            _{text{cleaner form}}
            end{array}
            ,.
            $$


          4. Iverson bracket:
            Iverson bracket notation, as suggested in @FredH's answer, is apparently the same thing; according to Wikipedia, it's meant as a generalization of the Kronecker delta, except they drop the $delta$ entirely, just putting the condition in square-brackets. In a context in readers expect it, Iverson bracket notation might be preferable if conditionals will be used a lot.





          Note: "Conditional operator" rather than "ternary operator".



          The conditional operator, condition ? trueValue : falseValue, has 3 arguments, making it an example of a ternary operator. By contrast, most other operators in programming tend to be unary operators (which have 1 argument) or binary operators (which have 2 arguments).



          Since the conditional operator is fairly unique in being a ternary operator, it's often been called "the ternary operator", leading many to believe that that's its name. However, "conditional operator" is more specific and should generally be preferred.






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
            $endgroup$
            – dataphile
            2 days ago










          • $begingroup$
            @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
            $endgroup$
            – Nat
            2 days ago








          • 2




            $begingroup$
            The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago








          • 1




            $begingroup$
            The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
            $endgroup$
            – J.G.
            2 days ago






          • 1




            $begingroup$
            Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
            $endgroup$
            – Nat
            yesterday














          59












          59








          59





          $begingroup$

          From physics, I'm used to seeing the Kronecker delta,$$
          {delta}_{ij}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & i=j \
          0 &text{else}
          end{array}
          right. _{,}
          $$
          and I think people who work with it find the slightly generalized notation$$
          {delta}_{left[text{condition}right]}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & left[text{condition}right] \
          0 &text{else}
          end{array}
          right.
          $$
          to be pretty natural to them.



          So, I tend to use $delta_{left[text{condition}right]}$ for a lot of things. Just seems so simple and well-understood.



          Transforms:




          1. Basic Kronecker delta:
            To write the basic Kronecker delta in terms of the generalized Kronecker delta, it's just$$
            delta_{ij}
            Rightarrow
            delta_{i=j}
            ,.$$
            It's almost the same notation, and I think most folks can figure it out pretty easily without needing it explained.


          2. Conditional operator:
            The "conditional operator" or "ternary operator" for the simple case of ?1:0:$$
            begin{array}{ccccc}
            boxed{
            begin{array}{l}
            texttt{if}~left(texttt{condition}right) \
            { \
            ~~~~texttt{return 1;} \
            } \
            texttt{else} \
            { \
            ~~~~texttt{return 0;} \
            }
            end{array}
            ~} &
            Rightarrow &
            boxed{~
            texttt{condition ? 1 : 0}
            ~} &
            Rightarrow &
            delta_{i=j}
            end{array}
            _{.}
            $$
            Then if you want a non-zero value for the false-case, you'd just add another Kronecker delta, $delta_{operatorname{NOT}left(left[text{condition}right]right)} ,$ e.g. $delta_{i neq j} .$


          3. Indicator function:
            @SiongThyeGoh's answer recommended using indicator function notation. I'd rewrite their example like$$
            begin{array}{ccccc}
            underbrace{a=b+1+mathbb{1}_{(-infty, 0]}(c)}
            _{text{their example}}
            &
            Rightarrow &
            underbrace{a=b+1+ delta_{c in left(-infty, 0right]}}
            _{text{direct translation}} &
            Rightarrow &
            underbrace{a=b+1+ delta_{c , {small{leq}} , 0}}
            _{text{cleaner form}}
            end{array}
            ,.
            $$


          4. Iverson bracket:
            Iverson bracket notation, as suggested in @FredH's answer, is apparently the same thing; according to Wikipedia, it's meant as a generalization of the Kronecker delta, except they drop the $delta$ entirely, just putting the condition in square-brackets. In a context in readers expect it, Iverson bracket notation might be preferable if conditionals will be used a lot.





          Note: "Conditional operator" rather than "ternary operator".



          The conditional operator, condition ? trueValue : falseValue, has 3 arguments, making it an example of a ternary operator. By contrast, most other operators in programming tend to be unary operators (which have 1 argument) or binary operators (which have 2 arguments).



          Since the conditional operator is fairly unique in being a ternary operator, it's often been called "the ternary operator", leading many to believe that that's its name. However, "conditional operator" is more specific and should generally be preferred.






          share|cite|improve this answer











          $endgroup$



          From physics, I'm used to seeing the Kronecker delta,$$
          {delta}_{ij}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & i=j \
          0 &text{else}
          end{array}
          right. _{,}
          $$
          and I think people who work with it find the slightly generalized notation$$
          {delta}_{left[text{condition}right]}
          equiv
          left{
          begin{array}{lll}
          1 &text{if} & left[text{condition}right] \
          0 &text{else}
          end{array}
          right.
          $$
          to be pretty natural to them.



          So, I tend to use $delta_{left[text{condition}right]}$ for a lot of things. Just seems so simple and well-understood.



          Transforms:




          1. Basic Kronecker delta:
            To write the basic Kronecker delta in terms of the generalized Kronecker delta, it's just$$
            delta_{ij}
            Rightarrow
            delta_{i=j}
            ,.$$
            It's almost the same notation, and I think most folks can figure it out pretty easily without needing it explained.


          2. Conditional operator:
            The "conditional operator" or "ternary operator" for the simple case of ?1:0:$$
            begin{array}{ccccc}
            boxed{
            begin{array}{l}
            texttt{if}~left(texttt{condition}right) \
            { \
            ~~~~texttt{return 1;} \
            } \
            texttt{else} \
            { \
            ~~~~texttt{return 0;} \
            }
            end{array}
            ~} &
            Rightarrow &
            boxed{~
            texttt{condition ? 1 : 0}
            ~} &
            Rightarrow &
            delta_{i=j}
            end{array}
            _{.}
            $$
            Then if you want a non-zero value for the false-case, you'd just add another Kronecker delta, $delta_{operatorname{NOT}left(left[text{condition}right]right)} ,$ e.g. $delta_{i neq j} .$


          3. Indicator function:
            @SiongThyeGoh's answer recommended using indicator function notation. I'd rewrite their example like$$
            begin{array}{ccccc}
            underbrace{a=b+1+mathbb{1}_{(-infty, 0]}(c)}
            _{text{their example}}
            &
            Rightarrow &
            underbrace{a=b+1+ delta_{c in left(-infty, 0right]}}
            _{text{direct translation}} &
            Rightarrow &
            underbrace{a=b+1+ delta_{c , {small{leq}} , 0}}
            _{text{cleaner form}}
            end{array}
            ,.
            $$


          4. Iverson bracket:
            Iverson bracket notation, as suggested in @FredH's answer, is apparently the same thing; according to Wikipedia, it's meant as a generalization of the Kronecker delta, except they drop the $delta$ entirely, just putting the condition in square-brackets. In a context in readers expect it, Iverson bracket notation might be preferable if conditionals will be used a lot.





          Note: "Conditional operator" rather than "ternary operator".



          The conditional operator, condition ? trueValue : falseValue, has 3 arguments, making it an example of a ternary operator. By contrast, most other operators in programming tend to be unary operators (which have 1 argument) or binary operators (which have 2 arguments).



          Since the conditional operator is fairly unique in being a ternary operator, it's often been called "the ternary operator", leading many to believe that that's its name. However, "conditional operator" is more specific and should generally be preferred.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 2 days ago

























          answered 2 days ago









          NatNat

          1,0581713




          1,0581713








          • 1




            $begingroup$
            wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
            $endgroup$
            – dataphile
            2 days ago










          • $begingroup$
            @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
            $endgroup$
            – Nat
            2 days ago








          • 2




            $begingroup$
            The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago








          • 1




            $begingroup$
            The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
            $endgroup$
            – J.G.
            2 days ago






          • 1




            $begingroup$
            Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
            $endgroup$
            – Nat
            yesterday














          • 1




            $begingroup$
            wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
            $endgroup$
            – dataphile
            2 days ago










          • $begingroup$
            @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
            $endgroup$
            – Nat
            2 days ago








          • 2




            $begingroup$
            The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago








          • 1




            $begingroup$
            The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
            $endgroup$
            – J.G.
            2 days ago






          • 1




            $begingroup$
            Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
            $endgroup$
            – Nat
            yesterday








          1




          1




          $begingroup$
          wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
          $endgroup$
          – dataphile
          2 days ago




          $begingroup$
          wow, this is beautiful. I need it for an infinite series (with some elements excluded i.e. multiplied by zero and others included, multiplied by 1) so this cleaner form is exactly what I need.
          $endgroup$
          – dataphile
          2 days ago












          $begingroup$
          @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
          $endgroup$
          – Nat
          2 days ago






          $begingroup$
          @dataphile Yeah, the Kronecker delta's great for specifying elements like that; it comes in handy if you're using Sigma/Pi/Einstein notations. Worth noting that it's basically the integrated Dirac delta; if you're working in a continuous domain, then the Dirac delta tends to be preferred, though it's largely the same thing.
          $endgroup$
          – Nat
          2 days ago






          2




          2




          $begingroup$
          The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
          $endgroup$
          – Konrad Rudolph
          2 days ago






          $begingroup$
          The Kronecker delta isn’t a ternary operator, it’s a plain old binary operator, since it has two operands.
          $endgroup$
          – Konrad Rudolph
          2 days ago






          1




          1




          $begingroup$
          The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
          $endgroup$
          – J.G.
          2 days ago




          $begingroup$
          The $1$-if-condition-else-$0$ generalisation of the Kronecker delta is called the Iverson bracket. We can generalise to any two input values we like with a suitable function, of domain ${0,,1}$, wraping the Iverson bracket.
          $endgroup$
          – J.G.
          2 days ago




          1




          1




          $begingroup$
          Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
          $endgroup$
          – Nat
          yesterday




          $begingroup$
          Tangentially, folks really need to get over the "ternary operator" thing. It's a common name, if a misnomer, in programming; it's a strawman to misattribute the general definition to the question statement when it's clearly not what they meant. Further, arity's arbitrary anyway; we may as well say that the addition operator, $`` + " ,$ is actually unary because it doesn't act on two addends but rather the tuple of them. Like in counting degrees of freedom or assigning entropy, just pick some sensible convention and understand it to be subjective.
          $endgroup$
          – Nat
          yesterday











          59












          $begingroup$

          The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly define a function
          $$f(b,c)=begin {cases} b+1&c gt 0\
          b+2 & c le 0 end {cases}$$



          You can also define functions with any number of inputs you want, so you can define $f(a,b,c)=a(b+c^2)$, for example. This is a ternary function.






          share|cite|improve this answer











          $endgroup$









          • 14




            $begingroup$
            Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
            $endgroup$
            – Džuris
            2 days ago






          • 19




            $begingroup$
            @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
            $endgroup$
            – frabala
            2 days ago






          • 21




            $begingroup$
            Once again, clarity beats compactness when it comes to mathematics.
            $endgroup$
            – Asaf Karagila
            2 days ago






          • 8




            $begingroup$
            Well-chosen compact notations can contribute to clarity rather than detract from it, though.
            $endgroup$
            – Henning Makholm
            2 days ago






          • 7




            $begingroup$
            @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
            $endgroup$
            – Konrad Rudolph
            2 days ago


















          59












          $begingroup$

          The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly define a function
          $$f(b,c)=begin {cases} b+1&c gt 0\
          b+2 & c le 0 end {cases}$$



          You can also define functions with any number of inputs you want, so you can define $f(a,b,c)=a(b+c^2)$, for example. This is a ternary function.






          share|cite|improve this answer











          $endgroup$









          • 14




            $begingroup$
            Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
            $endgroup$
            – Džuris
            2 days ago






          • 19




            $begingroup$
            @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
            $endgroup$
            – frabala
            2 days ago






          • 21




            $begingroup$
            Once again, clarity beats compactness when it comes to mathematics.
            $endgroup$
            – Asaf Karagila
            2 days ago






          • 8




            $begingroup$
            Well-chosen compact notations can contribute to clarity rather than detract from it, though.
            $endgroup$
            – Henning Makholm
            2 days ago






          • 7




            $begingroup$
            @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
            $endgroup$
            – Konrad Rudolph
            2 days ago
















          59












          59








          59





          $begingroup$

          The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly define a function
          $$f(b,c)=begin {cases} b+1&c gt 0\
          b+2 & c le 0 end {cases}$$



          You can also define functions with any number of inputs you want, so you can define $f(a,b,c)=a(b+c^2)$, for example. This is a ternary function.






          share|cite|improve this answer











          $endgroup$



          The expression b + (c > 0 ? 1 : 2) is not a ternary operator; it is a function of two variables. There is one operation that results in $a$. You can certainly define a function
          $$f(b,c)=begin {cases} b+1&c gt 0\
          b+2 & c le 0 end {cases}$$



          You can also define functions with any number of inputs you want, so you can define $f(a,b,c)=a(b+c^2)$, for example. This is a ternary function.







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited yesterday









          J. W. Tanner

          2,8421217




          2,8421217










          answered Mar 5 at 5:40









          Ross MillikanRoss Millikan

          299k24200374




          299k24200374








          • 14




            $begingroup$
            Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
            $endgroup$
            – Džuris
            2 days ago






          • 19




            $begingroup$
            @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
            $endgroup$
            – frabala
            2 days ago






          • 21




            $begingroup$
            Once again, clarity beats compactness when it comes to mathematics.
            $endgroup$
            – Asaf Karagila
            2 days ago






          • 8




            $begingroup$
            Well-chosen compact notations can contribute to clarity rather than detract from it, though.
            $endgroup$
            – Henning Makholm
            2 days ago






          • 7




            $begingroup$
            @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
            $endgroup$
            – Konrad Rudolph
            2 days ago
















          • 14




            $begingroup$
            Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
            $endgroup$
            – Džuris
            2 days ago






          • 19




            $begingroup$
            @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
            $endgroup$
            – frabala
            2 days ago






          • 21




            $begingroup$
            Once again, clarity beats compactness when it comes to mathematics.
            $endgroup$
            – Asaf Karagila
            2 days ago






          • 8




            $begingroup$
            Well-chosen compact notations can contribute to clarity rather than detract from it, though.
            $endgroup$
            – Henning Makholm
            2 days ago






          • 7




            $begingroup$
            @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
            $endgroup$
            – Konrad Rudolph
            2 days ago










          14




          14




          $begingroup$
          Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
          $endgroup$
          – Džuris
          2 days ago




          $begingroup$
          Ternary operator in programming means a conditional statement of form "if A then x else y" and uually is written just as presented in the OP, i.e. A ? x : y. It would also literally be termary if the OP wouldn't have inserted the particular values of 1 and 2.
          $endgroup$
          – Džuris
          2 days ago




          19




          19




          $begingroup$
          @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
          $endgroup$
          – frabala
          2 days ago




          $begingroup$
          @Džuris Ternary means "of arity 3", like binary means "of arity 2" and unary "of arity 1". The specific operator is the conditional ternary operator.
          $endgroup$
          – frabala
          2 days ago




          21




          21




          $begingroup$
          Once again, clarity beats compactness when it comes to mathematics.
          $endgroup$
          – Asaf Karagila
          2 days ago




          $begingroup$
          Once again, clarity beats compactness when it comes to mathematics.
          $endgroup$
          – Asaf Karagila
          2 days ago




          8




          8




          $begingroup$
          Well-chosen compact notations can contribute to clarity rather than detract from it, though.
          $endgroup$
          – Henning Makholm
          2 days ago




          $begingroup$
          Well-chosen compact notations can contribute to clarity rather than detract from it, though.
          $endgroup$
          – Henning Makholm
          2 days ago




          7




          7




          $begingroup$
          @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
          $endgroup$
          – Konrad Rudolph
          2 days ago






          $begingroup$
          @Džuris No it isn’t. The link you cite says, in its very first sentence, that “?: is a ternary operator” (not “the ternary operator”; emphasis mine). Some people refer to it as “the ternary operator” but this is strictly incorrect (and merits a correction e.g. on Stack Overflow).
          $endgroup$
          – Konrad Rudolph
          2 days ago













          40












          $begingroup$

          In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. Using this notation, you could write
          $$
          a = b + 2 - [c gt 0].
          $$






          share|cite|improve this answer











          $endgroup$









          • 7




            $begingroup$
            aka en.wikipedia.org/wiki/Iverson_bracket
            $endgroup$
            – qwr
            2 days ago






          • 6




            $begingroup$
            I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
            $endgroup$
            – Rahul
            2 days ago








          • 5




            $begingroup$
            I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
            $endgroup$
            – J. M. is not a mathematician
            2 days ago






          • 4




            $begingroup$
            Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
            $endgroup$
            – pipe
            2 days ago








          • 2




            $begingroup$
            Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
            $endgroup$
            – safkan
            23 hours ago
















          40












          $begingroup$

          In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. Using this notation, you could write
          $$
          a = b + 2 - [c gt 0].
          $$






          share|cite|improve this answer











          $endgroup$









          • 7




            $begingroup$
            aka en.wikipedia.org/wiki/Iverson_bracket
            $endgroup$
            – qwr
            2 days ago






          • 6




            $begingroup$
            I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
            $endgroup$
            – Rahul
            2 days ago








          • 5




            $begingroup$
            I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
            $endgroup$
            – J. M. is not a mathematician
            2 days ago






          • 4




            $begingroup$
            Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
            $endgroup$
            – pipe
            2 days ago








          • 2




            $begingroup$
            Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
            $endgroup$
            – safkan
            23 hours ago














          40












          40








          40





          $begingroup$

          In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. Using this notation, you could write
          $$
          a = b + 2 - [c gt 0].
          $$






          share|cite|improve this answer











          $endgroup$



          In Concrete Mathematics by Graham, Knuth and Patashnik, the authors use the "Iverson bracket" notation: Square brackets around a statement represent $1$ if the statement is true and $0$ otherwise. Using this notation, you could write
          $$
          a = b + 2 - [c gt 0].
          $$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 2 days ago

























          answered 2 days ago









          FredHFredH

          1,048612




          1,048612








          • 7




            $begingroup$
            aka en.wikipedia.org/wiki/Iverson_bracket
            $endgroup$
            – qwr
            2 days ago






          • 6




            $begingroup$
            I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
            $endgroup$
            – Rahul
            2 days ago








          • 5




            $begingroup$
            I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
            $endgroup$
            – J. M. is not a mathematician
            2 days ago






          • 4




            $begingroup$
            Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
            $endgroup$
            – pipe
            2 days ago








          • 2




            $begingroup$
            Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
            $endgroup$
            – safkan
            23 hours ago














          • 7




            $begingroup$
            aka en.wikipedia.org/wiki/Iverson_bracket
            $endgroup$
            – qwr
            2 days ago






          • 6




            $begingroup$
            I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
            $endgroup$
            – Rahul
            2 days ago








          • 5




            $begingroup$
            I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
            $endgroup$
            – J. M. is not a mathematician
            2 days ago






          • 4




            $begingroup$
            Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
            $endgroup$
            – pipe
            2 days ago








          • 2




            $begingroup$
            Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
            $endgroup$
            – safkan
            23 hours ago








          7




          7




          $begingroup$
          aka en.wikipedia.org/wiki/Iverson_bracket
          $endgroup$
          – qwr
          2 days ago




          $begingroup$
          aka en.wikipedia.org/wiki/Iverson_bracket
          $endgroup$
          – qwr
          2 days ago




          6




          6




          $begingroup$
          I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
          $endgroup$
          – Rahul
          2 days ago






          $begingroup$
          I would find it clearer to write $a = b + 1[c>0] + 2[cle0]$.
          $endgroup$
          – Rahul
          2 days ago






          5




          5




          $begingroup$
          I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
          $endgroup$
          – J. M. is not a mathematician
          2 days ago




          $begingroup$
          I personally find Iverson brackets less cluttered than indicator functions, so I definitely recommend this notation.
          $endgroup$
          – J. M. is not a mathematician
          2 days ago




          4




          4




          $begingroup$
          Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
          $endgroup$
          – pipe
          2 days ago






          $begingroup$
          Surely this is a unary operator, which works much like for example ! in the C programming language: Input is an arbitrary expression, the result is either 0 or 1 depending on the expression.
          $endgroup$
          – pipe
          2 days ago






          2




          2




          $begingroup$
          Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
          $endgroup$
          – safkan
          23 hours ago




          $begingroup$
          Interesting note: Iverson, in his original book, used parentheses (x>0) and not brackets [x>0]. Apparently, it was Knuth and Patashnik that converted it into brackets; and they called it the "Iverson bracket".
          $endgroup$
          – safkan
          23 hours ago











          24












          $begingroup$

          Using the indicator function notation:$$a=b+1+mathbb{1}_{(-infty, 0]}(c)$$






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            Indicator is definitely the way to go, since the conditional can define an arbitrary set.
            $endgroup$
            – eyeballfrog
            Mar 5 at 5:47










          • $begingroup$
            Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
            $endgroup$
            – dataphile
            Mar 5 at 5:52






          • 2




            $begingroup$
            I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
            $endgroup$
            – Christopher
            2 days ago








          • 1




            $begingroup$
            The indicator function isn’t a ternary operator, it only has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago












          • $begingroup$
            I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
            $endgroup$
            – David Richerby
            18 hours ago
















          24












          $begingroup$

          Using the indicator function notation:$$a=b+1+mathbb{1}_{(-infty, 0]}(c)$$






          share|cite|improve this answer











          $endgroup$









          • 1




            $begingroup$
            Indicator is definitely the way to go, since the conditional can define an arbitrary set.
            $endgroup$
            – eyeballfrog
            Mar 5 at 5:47










          • $begingroup$
            Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
            $endgroup$
            – dataphile
            Mar 5 at 5:52






          • 2




            $begingroup$
            I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
            $endgroup$
            – Christopher
            2 days ago








          • 1




            $begingroup$
            The indicator function isn’t a ternary operator, it only has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago












          • $begingroup$
            I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
            $endgroup$
            – David Richerby
            18 hours ago














          24












          24








          24





          $begingroup$

          Using the indicator function notation:$$a=b+1+mathbb{1}_{(-infty, 0]}(c)$$






          share|cite|improve this answer











          $endgroup$



          Using the indicator function notation:$$a=b+1+mathbb{1}_{(-infty, 0]}(c)$$







          share|cite|improve this answer














          share|cite|improve this answer



          share|cite|improve this answer








          edited 2 days ago

























          answered Mar 5 at 5:34









          Siong Thye GohSiong Thye Goh

          102k1467119




          102k1467119








          • 1




            $begingroup$
            Indicator is definitely the way to go, since the conditional can define an arbitrary set.
            $endgroup$
            – eyeballfrog
            Mar 5 at 5:47










          • $begingroup$
            Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
            $endgroup$
            – dataphile
            Mar 5 at 5:52






          • 2




            $begingroup$
            I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
            $endgroup$
            – Christopher
            2 days ago








          • 1




            $begingroup$
            The indicator function isn’t a ternary operator, it only has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago












          • $begingroup$
            I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
            $endgroup$
            – David Richerby
            18 hours ago














          • 1




            $begingroup$
            Indicator is definitely the way to go, since the conditional can define an arbitrary set.
            $endgroup$
            – eyeballfrog
            Mar 5 at 5:47










          • $begingroup$
            Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
            $endgroup$
            – dataphile
            Mar 5 at 5:52






          • 2




            $begingroup$
            I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
            $endgroup$
            – Christopher
            2 days ago








          • 1




            $begingroup$
            The indicator function isn’t a ternary operator, it only has two operands.
            $endgroup$
            – Konrad Rudolph
            2 days ago












          • $begingroup$
            I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
            $endgroup$
            – David Richerby
            18 hours ago








          1




          1




          $begingroup$
          Indicator is definitely the way to go, since the conditional can define an arbitrary set.
          $endgroup$
          – eyeballfrog
          Mar 5 at 5:47




          $begingroup$
          Indicator is definitely the way to go, since the conditional can define an arbitrary set.
          $endgroup$
          – eyeballfrog
          Mar 5 at 5:47












          $begingroup$
          Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
          $endgroup$
          – dataphile
          Mar 5 at 5:52




          $begingroup$
          Thank you, that is very elegant. I will definitely try out all of the answers as I often use this in various scenarios.
          $endgroup$
          – dataphile
          Mar 5 at 5:52




          2




          2




          $begingroup$
          I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
          $endgroup$
          – Christopher
          2 days ago






          $begingroup$
          I often use - and have seen others use - $mathbb{1}$ ("blackboard bold") to denote the indicator function to distinguish it from the number $1$
          $endgroup$
          – Christopher
          2 days ago






          1




          1




          $begingroup$
          The indicator function isn’t a ternary operator, it only has two operands.
          $endgroup$
          – Konrad Rudolph
          2 days ago






          $begingroup$
          The indicator function isn’t a ternary operator, it only has two operands.
          $endgroup$
          – Konrad Rudolph
          2 days ago














          $begingroup$
          I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
          $endgroup$
          – David Richerby
          18 hours ago




          $begingroup$
          I don't understand what your indicator means. I've only ever seen indicators used as $1_X$, where $X$ is a true/false-valued expression, so I'd write your indicator as $1_{c<0}$.
          $endgroup$
          – David Richerby
          18 hours ago











          14












          $begingroup$

          In math, equations are written in piecewise form by having a curly brace enclose multiple lines; each one with a condition excepting the last which has "otherwise".



          There are a few custom operators that also occasionally make an appearance. E.g. the Heavyside function mentioned by Alex, the Dirac function, and the cyclical operator $delta_{ijk}$ - all of which can be used to emulate conditional behaviour.






          share|cite|improve this answer









          $endgroup$


















            14












            $begingroup$

            In math, equations are written in piecewise form by having a curly brace enclose multiple lines; each one with a condition excepting the last which has "otherwise".



            There are a few custom operators that also occasionally make an appearance. E.g. the Heavyside function mentioned by Alex, the Dirac function, and the cyclical operator $delta_{ijk}$ - all of which can be used to emulate conditional behaviour.






            share|cite|improve this answer









            $endgroup$
















              14












              14








              14





              $begingroup$

              In math, equations are written in piecewise form by having a curly brace enclose multiple lines; each one with a condition excepting the last which has "otherwise".



              There are a few custom operators that also occasionally make an appearance. E.g. the Heavyside function mentioned by Alex, the Dirac function, and the cyclical operator $delta_{ijk}$ - all of which can be used to emulate conditional behaviour.






              share|cite|improve this answer









              $endgroup$



              In math, equations are written in piecewise form by having a curly brace enclose multiple lines; each one with a condition excepting the last which has "otherwise".



              There are a few custom operators that also occasionally make an appearance. E.g. the Heavyside function mentioned by Alex, the Dirac function, and the cyclical operator $delta_{ijk}$ - all of which can be used to emulate conditional behaviour.







              share|cite|improve this answer












              share|cite|improve this answer



              share|cite|improve this answer










              answered Mar 5 at 5:35









              Paul ChildsPaul Childs

              4328




              4328























                  5












                  $begingroup$

                  One should realize that operators are just a fancy way of using functions.
                  So a ternary operator is a function of 3 variables that is notated in a different way. Is that useful? The answer is mostly not. Also realize that any mathematician is allowed to introduce any notation he feels is illustrative.



                  Let's review why we use binary operators at all like in a+b*c . Because parameters and results are of the same type, it makes sense to leave out parentheses and introduce complicated priority rules. Imagine that a b c are numbers and we have a normal + and a peculiar * that results in dragons. Now the expression doesn't make sense (assumming a high priority *), because there is no way to add numbers and dragons. Thusly most ternary operators results in a mess.



                  With a proper notation there are examples of ternary operations. For example, there is a special notation for "sum for i from a to b of expression". This takes two boundaries (numbers) and a function from a number of that type that results in another number. (Mathematician, read "element of an addition group" for number.)
                  The notation for integration is similarly ternary.

                  So in short ternary operators exist, and you can define your own. They are in general accompagnied with a special notation, or they are not helpful.



                  Now back to the special case you mention.
                  Because truth values are implied in math, an expression like "if a then b else c" makes sense if a represens a truth value like (7<12). The above expression is understood in every mathematical context. However in a context where truth values are not considered a set, (if .. then .. else ..) would not be considered an operator/function, but a textual explanation. A general accepted notation could be useful in math, but I'm not aware there is one. That is probably, because like in the above, informal notations are readily understood.






                  share|cite|improve this answer









                  $endgroup$


















                    5












                    $begingroup$

                    One should realize that operators are just a fancy way of using functions.
                    So a ternary operator is a function of 3 variables that is notated in a different way. Is that useful? The answer is mostly not. Also realize that any mathematician is allowed to introduce any notation he feels is illustrative.



                    Let's review why we use binary operators at all like in a+b*c . Because parameters and results are of the same type, it makes sense to leave out parentheses and introduce complicated priority rules. Imagine that a b c are numbers and we have a normal + and a peculiar * that results in dragons. Now the expression doesn't make sense (assumming a high priority *), because there is no way to add numbers and dragons. Thusly most ternary operators results in a mess.



                    With a proper notation there are examples of ternary operations. For example, there is a special notation for "sum for i from a to b of expression". This takes two boundaries (numbers) and a function from a number of that type that results in another number. (Mathematician, read "element of an addition group" for number.)
                    The notation for integration is similarly ternary.

                    So in short ternary operators exist, and you can define your own. They are in general accompagnied with a special notation, or they are not helpful.



                    Now back to the special case you mention.
                    Because truth values are implied in math, an expression like "if a then b else c" makes sense if a represens a truth value like (7<12). The above expression is understood in every mathematical context. However in a context where truth values are not considered a set, (if .. then .. else ..) would not be considered an operator/function, but a textual explanation. A general accepted notation could be useful in math, but I'm not aware there is one. That is probably, because like in the above, informal notations are readily understood.






                    share|cite|improve this answer









                    $endgroup$
















                      5












                      5








                      5





                      $begingroup$

                      One should realize that operators are just a fancy way of using functions.
                      So a ternary operator is a function of 3 variables that is notated in a different way. Is that useful? The answer is mostly not. Also realize that any mathematician is allowed to introduce any notation he feels is illustrative.



                      Let's review why we use binary operators at all like in a+b*c . Because parameters and results are of the same type, it makes sense to leave out parentheses and introduce complicated priority rules. Imagine that a b c are numbers and we have a normal + and a peculiar * that results in dragons. Now the expression doesn't make sense (assumming a high priority *), because there is no way to add numbers and dragons. Thusly most ternary operators results in a mess.



                      With a proper notation there are examples of ternary operations. For example, there is a special notation for "sum for i from a to b of expression". This takes two boundaries (numbers) and a function from a number of that type that results in another number. (Mathematician, read "element of an addition group" for number.)
                      The notation for integration is similarly ternary.

                      So in short ternary operators exist, and you can define your own. They are in general accompagnied with a special notation, or they are not helpful.



                      Now back to the special case you mention.
                      Because truth values are implied in math, an expression like "if a then b else c" makes sense if a represens a truth value like (7<12). The above expression is understood in every mathematical context. However in a context where truth values are not considered a set, (if .. then .. else ..) would not be considered an operator/function, but a textual explanation. A general accepted notation could be useful in math, but I'm not aware there is one. That is probably, because like in the above, informal notations are readily understood.






                      share|cite|improve this answer









                      $endgroup$



                      One should realize that operators are just a fancy way of using functions.
                      So a ternary operator is a function of 3 variables that is notated in a different way. Is that useful? The answer is mostly not. Also realize that any mathematician is allowed to introduce any notation he feels is illustrative.



                      Let's review why we use binary operators at all like in a+b*c . Because parameters and results are of the same type, it makes sense to leave out parentheses and introduce complicated priority rules. Imagine that a b c are numbers and we have a normal + and a peculiar * that results in dragons. Now the expression doesn't make sense (assumming a high priority *), because there is no way to add numbers and dragons. Thusly most ternary operators results in a mess.



                      With a proper notation there are examples of ternary operations. For example, there is a special notation for "sum for i from a to b of expression". This takes two boundaries (numbers) and a function from a number of that type that results in another number. (Mathematician, read "element of an addition group" for number.)
                      The notation for integration is similarly ternary.

                      So in short ternary operators exist, and you can define your own. They are in general accompagnied with a special notation, or they are not helpful.



                      Now back to the special case you mention.
                      Because truth values are implied in math, an expression like "if a then b else c" makes sense if a represens a truth value like (7<12). The above expression is understood in every mathematical context. However in a context where truth values are not considered a set, (if .. then .. else ..) would not be considered an operator/function, but a textual explanation. A general accepted notation could be useful in math, but I'm not aware there is one. That is probably, because like in the above, informal notations are readily understood.







                      share|cite|improve this answer












                      share|cite|improve this answer



                      share|cite|improve this answer










                      answered 2 days ago









                      Albert van der HorstAlbert van der Horst

                      20125




                      20125























                          5












                          $begingroup$

                          I think mathematicians should not be afraid to use the Iverson bracket, including when teaching, as this is a generally very useful notation whose only slightly unusual feature is to introduce a logical expression in the middle of an algebraic one (but one already regularly finds conditions inside set-theoretic expressions, so it really is not a big deal). It may avoid a lot of clutter, notably many instances of clumsy expressions by cases with a big unmatched brace (which is usually only usable as the right hand side of a definition). Since brackets do have many other uses in mathematics, I personally prefer a typographically distinct representation of Iverson brackets, rendering your example as
                          $$def[#1]{[![{#1}]!]}
                          a= b + [c>0]1 + [cnot>0]2.
                          $$

                          This works best in additive context (though one can use Iverson brackets in the exponent for optional multiplicative factors). It is not really ideal for general two-way branches, as the condition must be repeated twice, one of them in negated form, but it happens that most of the time one needs $0$ as the value for one branch anyway.



                          As a more concise two-way branch, I can recall that Algol68 introduced the notation $b+(c>0mid 1mid 2)$ for the right-hand side of your equation; though this is a programming language and not mathematics, it was designed by mathematicians. They also had notation for multi-way branching: thus the solution to the recursion $a_{n+2}=a_{n+1}-a_n$ with initial values $a_0=0$, $a_1=1$ can be written
                          $$
                          a_n=(nbmod 6+1mid 0,1,1,0,-1,-1)
                          $$

                          (where the "${}+1$" is needed because in 1968 they still counted starting from $1$, which is a mistake), which is reasonably concise and readable, compared to other ways to express this result. Also consider, for month $m$ in year $y$, the number
                          $$
                          ( m mid 31,(ybmod 4=0land ybmod 100neq0lor ybmod400=0mid 29mid 28)
                          ,31,30,31,30,31,31,30,31,30,31).
                          $$






                          share|cite|improve this answer









                          $endgroup$


















                            5












                            $begingroup$

                            I think mathematicians should not be afraid to use the Iverson bracket, including when teaching, as this is a generally very useful notation whose only slightly unusual feature is to introduce a logical expression in the middle of an algebraic one (but one already regularly finds conditions inside set-theoretic expressions, so it really is not a big deal). It may avoid a lot of clutter, notably many instances of clumsy expressions by cases with a big unmatched brace (which is usually only usable as the right hand side of a definition). Since brackets do have many other uses in mathematics, I personally prefer a typographically distinct representation of Iverson brackets, rendering your example as
                            $$def[#1]{[![{#1}]!]}
                            a= b + [c>0]1 + [cnot>0]2.
                            $$

                            This works best in additive context (though one can use Iverson brackets in the exponent for optional multiplicative factors). It is not really ideal for general two-way branches, as the condition must be repeated twice, one of them in negated form, but it happens that most of the time one needs $0$ as the value for one branch anyway.



                            As a more concise two-way branch, I can recall that Algol68 introduced the notation $b+(c>0mid 1mid 2)$ for the right-hand side of your equation; though this is a programming language and not mathematics, it was designed by mathematicians. They also had notation for multi-way branching: thus the solution to the recursion $a_{n+2}=a_{n+1}-a_n$ with initial values $a_0=0$, $a_1=1$ can be written
                            $$
                            a_n=(nbmod 6+1mid 0,1,1,0,-1,-1)
                            $$

                            (where the "${}+1$" is needed because in 1968 they still counted starting from $1$, which is a mistake), which is reasonably concise and readable, compared to other ways to express this result. Also consider, for month $m$ in year $y$, the number
                            $$
                            ( m mid 31,(ybmod 4=0land ybmod 100neq0lor ybmod400=0mid 29mid 28)
                            ,31,30,31,30,31,31,30,31,30,31).
                            $$






                            share|cite|improve this answer









                            $endgroup$
















                              5












                              5








                              5





                              $begingroup$

                              I think mathematicians should not be afraid to use the Iverson bracket, including when teaching, as this is a generally very useful notation whose only slightly unusual feature is to introduce a logical expression in the middle of an algebraic one (but one already regularly finds conditions inside set-theoretic expressions, so it really is not a big deal). It may avoid a lot of clutter, notably many instances of clumsy expressions by cases with a big unmatched brace (which is usually only usable as the right hand side of a definition). Since brackets do have many other uses in mathematics, I personally prefer a typographically distinct representation of Iverson brackets, rendering your example as
                              $$def[#1]{[![{#1}]!]}
                              a= b + [c>0]1 + [cnot>0]2.
                              $$

                              This works best in additive context (though one can use Iverson brackets in the exponent for optional multiplicative factors). It is not really ideal for general two-way branches, as the condition must be repeated twice, one of them in negated form, but it happens that most of the time one needs $0$ as the value for one branch anyway.



                              As a more concise two-way branch, I can recall that Algol68 introduced the notation $b+(c>0mid 1mid 2)$ for the right-hand side of your equation; though this is a programming language and not mathematics, it was designed by mathematicians. They also had notation for multi-way branching: thus the solution to the recursion $a_{n+2}=a_{n+1}-a_n$ with initial values $a_0=0$, $a_1=1$ can be written
                              $$
                              a_n=(nbmod 6+1mid 0,1,1,0,-1,-1)
                              $$

                              (where the "${}+1$" is needed because in 1968 they still counted starting from $1$, which is a mistake), which is reasonably concise and readable, compared to other ways to express this result. Also consider, for month $m$ in year $y$, the number
                              $$
                              ( m mid 31,(ybmod 4=0land ybmod 100neq0lor ybmod400=0mid 29mid 28)
                              ,31,30,31,30,31,31,30,31,30,31).
                              $$






                              share|cite|improve this answer









                              $endgroup$



                              I think mathematicians should not be afraid to use the Iverson bracket, including when teaching, as this is a generally very useful notation whose only slightly unusual feature is to introduce a logical expression in the middle of an algebraic one (but one already regularly finds conditions inside set-theoretic expressions, so it really is not a big deal). It may avoid a lot of clutter, notably many instances of clumsy expressions by cases with a big unmatched brace (which is usually only usable as the right hand side of a definition). Since brackets do have many other uses in mathematics, I personally prefer a typographically distinct representation of Iverson brackets, rendering your example as
                              $$def[#1]{[![{#1}]!]}
                              a= b + [c>0]1 + [cnot>0]2.
                              $$

                              This works best in additive context (though one can use Iverson brackets in the exponent for optional multiplicative factors). It is not really ideal for general two-way branches, as the condition must be repeated twice, one of them in negated form, but it happens that most of the time one needs $0$ as the value for one branch anyway.



                              As a more concise two-way branch, I can recall that Algol68 introduced the notation $b+(c>0mid 1mid 2)$ for the right-hand side of your equation; though this is a programming language and not mathematics, it was designed by mathematicians. They also had notation for multi-way branching: thus the solution to the recursion $a_{n+2}=a_{n+1}-a_n$ with initial values $a_0=0$, $a_1=1$ can be written
                              $$
                              a_n=(nbmod 6+1mid 0,1,1,0,-1,-1)
                              $$

                              (where the "${}+1$" is needed because in 1968 they still counted starting from $1$, which is a mistake), which is reasonably concise and readable, compared to other ways to express this result. Also consider, for month $m$ in year $y$, the number
                              $$
                              ( m mid 31,(ybmod 4=0land ybmod 100neq0lor ybmod400=0mid 29mid 28)
                              ,31,30,31,30,31,31,30,31,30,31).
                              $$







                              share|cite|improve this answer












                              share|cite|improve this answer



                              share|cite|improve this answer










                              answered yesterday









                              Marc van LeeuwenMarc van Leeuwen

                              87.9k5111226




                              87.9k5111226























                                  3












                                  $begingroup$

                                  The accepted answer from Nat, suggesting the Kronecker Delta, is correct. However, it is also important to note that one of the highly upvoted answers here, which claims the C ternary operator x?y:z is not ternary is incorrect.



                                  Mathematically, the expression x?y:z can be expressed as a function of three variables:
                                  $$f(x,y,z)=begin {cases} y&xneq 0\
                                  z & x=0 end {cases}$$



                                  Note that in programming an expression such as $a<b$ could be used for $x$. If the expression is true, then $x=1$, otherwise $x=0$.



                                  About nomenclature: computer programmers have used the phrase the ternary operator to mean exactly this since at least the 1970s. Of course, among mathematicians, it would simply be a ternary operator and we would qualify it by either stating a programming language, e.g., the C ternary operator, or by calling it the conditional operator.






                                  share|cite|improve this answer










                                  New contributor




                                  hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                  Check out our Code of Conduct.






                                  $endgroup$


















                                    3












                                    $begingroup$

                                    The accepted answer from Nat, suggesting the Kronecker Delta, is correct. However, it is also important to note that one of the highly upvoted answers here, which claims the C ternary operator x?y:z is not ternary is incorrect.



                                    Mathematically, the expression x?y:z can be expressed as a function of three variables:
                                    $$f(x,y,z)=begin {cases} y&xneq 0\
                                    z & x=0 end {cases}$$



                                    Note that in programming an expression such as $a<b$ could be used for $x$. If the expression is true, then $x=1$, otherwise $x=0$.



                                    About nomenclature: computer programmers have used the phrase the ternary operator to mean exactly this since at least the 1970s. Of course, among mathematicians, it would simply be a ternary operator and we would qualify it by either stating a programming language, e.g., the C ternary operator, or by calling it the conditional operator.






                                    share|cite|improve this answer










                                    New contributor




                                    hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                    Check out our Code of Conduct.






                                    $endgroup$
















                                      3












                                      3








                                      3





                                      $begingroup$

                                      The accepted answer from Nat, suggesting the Kronecker Delta, is correct. However, it is also important to note that one of the highly upvoted answers here, which claims the C ternary operator x?y:z is not ternary is incorrect.



                                      Mathematically, the expression x?y:z can be expressed as a function of three variables:
                                      $$f(x,y,z)=begin {cases} y&xneq 0\
                                      z & x=0 end {cases}$$



                                      Note that in programming an expression such as $a<b$ could be used for $x$. If the expression is true, then $x=1$, otherwise $x=0$.



                                      About nomenclature: computer programmers have used the phrase the ternary operator to mean exactly this since at least the 1970s. Of course, among mathematicians, it would simply be a ternary operator and we would qualify it by either stating a programming language, e.g., the C ternary operator, or by calling it the conditional operator.






                                      share|cite|improve this answer










                                      New contributor




                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.






                                      $endgroup$



                                      The accepted answer from Nat, suggesting the Kronecker Delta, is correct. However, it is also important to note that one of the highly upvoted answers here, which claims the C ternary operator x?y:z is not ternary is incorrect.



                                      Mathematically, the expression x?y:z can be expressed as a function of three variables:
                                      $$f(x,y,z)=begin {cases} y&xneq 0\
                                      z & x=0 end {cases}$$



                                      Note that in programming an expression such as $a<b$ could be used for $x$. If the expression is true, then $x=1$, otherwise $x=0$.



                                      About nomenclature: computer programmers have used the phrase the ternary operator to mean exactly this since at least the 1970s. Of course, among mathematicians, it would simply be a ternary operator and we would qualify it by either stating a programming language, e.g., the C ternary operator, or by calling it the conditional operator.







                                      share|cite|improve this answer










                                      New contributor




                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.









                                      share|cite|improve this answer



                                      share|cite|improve this answer








                                      edited 13 hours ago





















                                      New contributor




                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.









                                      answered 13 hours ago









                                      hackerb9hackerb9

                                      1394




                                      1394




                                      New contributor




                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.





                                      New contributor





                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.






                                      hackerb9 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                      Check out our Code of Conduct.























                                          1












                                          $begingroup$

                                          There are many good answers that give notation for, “if this condition holds, then 1, else 0.” This corresponds to an even simpler expression in C;(x>1) is equivalent to (x>1 ? 1 : 0).



                                          It’s worth noting that the ternary operator is more general than that. If the arguments are elements of a ring, you could express c ? a : b with (using Iverson-bracket notation) $(a-b) cdot [c] + b$, but not otherwise. (And compilers frequently use this trick, in a Boolean ring, to compile conditionals without needing to execute a branch instruction.) In a C program, evaluating the expressions $a$ or $b$ might have side-effects, such as deleting a file or printing a message to the screen. In a mathematical function, this isn’t something you would worry about, and a programming language where this is impossible is called functional.



                                          Ross Millikan gave the most standard notation, a cases block. The closest equivalent in mathematical computer science is the if-then-else function of Lambda Calculus.






                                          share|cite|improve this answer











                                          $endgroup$













                                          • $begingroup$
                                            "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                            $endgroup$
                                            – a CVn
                                            2 days ago






                                          • 1




                                            $begingroup$
                                            @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                            $endgroup$
                                            – Davislor
                                            2 days ago












                                          • $begingroup$
                                            @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                            $endgroup$
                                            – Davislor
                                            2 days ago
















                                          1












                                          $begingroup$

                                          There are many good answers that give notation for, “if this condition holds, then 1, else 0.” This corresponds to an even simpler expression in C;(x>1) is equivalent to (x>1 ? 1 : 0).



                                          It’s worth noting that the ternary operator is more general than that. If the arguments are elements of a ring, you could express c ? a : b with (using Iverson-bracket notation) $(a-b) cdot [c] + b$, but not otherwise. (And compilers frequently use this trick, in a Boolean ring, to compile conditionals without needing to execute a branch instruction.) In a C program, evaluating the expressions $a$ or $b$ might have side-effects, such as deleting a file or printing a message to the screen. In a mathematical function, this isn’t something you would worry about, and a programming language where this is impossible is called functional.



                                          Ross Millikan gave the most standard notation, a cases block. The closest equivalent in mathematical computer science is the if-then-else function of Lambda Calculus.






                                          share|cite|improve this answer











                                          $endgroup$













                                          • $begingroup$
                                            "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                            $endgroup$
                                            – a CVn
                                            2 days ago






                                          • 1




                                            $begingroup$
                                            @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                            $endgroup$
                                            – Davislor
                                            2 days ago












                                          • $begingroup$
                                            @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                            $endgroup$
                                            – Davislor
                                            2 days ago














                                          1












                                          1








                                          1





                                          $begingroup$

                                          There are many good answers that give notation for, “if this condition holds, then 1, else 0.” This corresponds to an even simpler expression in C;(x>1) is equivalent to (x>1 ? 1 : 0).



                                          It’s worth noting that the ternary operator is more general than that. If the arguments are elements of a ring, you could express c ? a : b with (using Iverson-bracket notation) $(a-b) cdot [c] + b$, but not otherwise. (And compilers frequently use this trick, in a Boolean ring, to compile conditionals without needing to execute a branch instruction.) In a C program, evaluating the expressions $a$ or $b$ might have side-effects, such as deleting a file or printing a message to the screen. In a mathematical function, this isn’t something you would worry about, and a programming language where this is impossible is called functional.



                                          Ross Millikan gave the most standard notation, a cases block. The closest equivalent in mathematical computer science is the if-then-else function of Lambda Calculus.






                                          share|cite|improve this answer











                                          $endgroup$



                                          There are many good answers that give notation for, “if this condition holds, then 1, else 0.” This corresponds to an even simpler expression in C;(x>1) is equivalent to (x>1 ? 1 : 0).



                                          It’s worth noting that the ternary operator is more general than that. If the arguments are elements of a ring, you could express c ? a : b with (using Iverson-bracket notation) $(a-b) cdot [c] + b$, but not otherwise. (And compilers frequently use this trick, in a Boolean ring, to compile conditionals without needing to execute a branch instruction.) In a C program, evaluating the expressions $a$ or $b$ might have side-effects, such as deleting a file or printing a message to the screen. In a mathematical function, this isn’t something you would worry about, and a programming language where this is impossible is called functional.



                                          Ross Millikan gave the most standard notation, a cases block. The closest equivalent in mathematical computer science is the if-then-else function of Lambda Calculus.







                                          share|cite|improve this answer














                                          share|cite|improve this answer



                                          share|cite|improve this answer








                                          edited 2 days ago

























                                          answered 2 days ago









                                          DavislorDavislor

                                          2,360815




                                          2,360815












                                          • $begingroup$
                                            "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                            $endgroup$
                                            – a CVn
                                            2 days ago






                                          • 1




                                            $begingroup$
                                            @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                            $endgroup$
                                            – Davislor
                                            2 days ago












                                          • $begingroup$
                                            @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                            $endgroup$
                                            – Davislor
                                            2 days ago


















                                          • $begingroup$
                                            "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                            $endgroup$
                                            – a CVn
                                            2 days ago






                                          • 1




                                            $begingroup$
                                            @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                            $endgroup$
                                            – Davislor
                                            2 days ago












                                          • $begingroup$
                                            @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                            $endgroup$
                                            – Davislor
                                            2 days ago
















                                          $begingroup$
                                          "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                          $endgroup$
                                          – a CVn
                                          2 days ago




                                          $begingroup$
                                          "in C;(x>1) is equivalent to (x>1 ? 1 : 0)" Not exactly. Rather, C considers any nonzero value as equivalent from a truthiness perspective. So there is no difference between an integer expression taking the value of -1, 1, 42 or INT_MAX when that expression is treated as a boolean rvalue. In C, the one special integer value, when treated as a boolean, is 0, representing false. That said, if someone actually used (x>1) as a non-boolean expression and I noticed it, I would likely at least briefly try to find some heavy physical object that could be applied at high speed to their keyboard.
                                          $endgroup$
                                          – a CVn
                                          2 days ago




                                          1




                                          1




                                          $begingroup$
                                          @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                          $endgroup$
                                          – Davislor
                                          2 days ago






                                          $begingroup$
                                          @aCVn The C11 standard states, “Each of the operators < (less than), > (greater than), <= (less than or equal to), and >= (greater than or equal to) shall yield 1 if the specified relation is true and 0 if it is false.” Similarly for equality and inequality, “Each of the operators yields 1 if the specified relation is true and 0 if it is false.”
                                          $endgroup$
                                          – Davislor
                                          2 days ago














                                          $begingroup$
                                          @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                          $endgroup$
                                          – Davislor
                                          2 days ago




                                          $begingroup$
                                          @aCVn What you wrote is true, but the relational operators in C will only return the values 1 or 0.
                                          $endgroup$
                                          – Davislor
                                          2 days ago











                                          1












                                          $begingroup$

                                          Following solution is not defined for $c = 0$; however it uses very basic operations only, which might be useful as you probably look for an expression to implement in a program:



                                          $$a = b + 1lambda + 2(1-lambda)$$



                                          where



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$





                                          You need to make the problem discrete and make a choice from two values. So, given some value $c in mathbb{R}$ we need to calculate some value $lambda in {0,1}$ depnding on $c<0$ or $c>0$.



                                          Knowing that



                                          $$frac{|c|}{c} in {1,-1}$$



                                          we can calculate the $lambda$ as follows:



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$



                                          Now that our $lambda in {0,1}$ we can do the "choice" between the two constants $d$ and $e$ as follows:



                                          $$dlambda + e(1-lambda)$$



                                          which equals $d$ for $lambda = 1$, and $e$ for $lambda = 0$.






                                          share|cite|improve this answer










                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.






                                          $endgroup$













                                          • $begingroup$
                                            And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                            $endgroup$
                                            – David Richerby
                                            18 hours ago
















                                          1












                                          $begingroup$

                                          Following solution is not defined for $c = 0$; however it uses very basic operations only, which might be useful as you probably look for an expression to implement in a program:



                                          $$a = b + 1lambda + 2(1-lambda)$$



                                          where



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$





                                          You need to make the problem discrete and make a choice from two values. So, given some value $c in mathbb{R}$ we need to calculate some value $lambda in {0,1}$ depnding on $c<0$ or $c>0$.



                                          Knowing that



                                          $$frac{|c|}{c} in {1,-1}$$



                                          we can calculate the $lambda$ as follows:



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$



                                          Now that our $lambda in {0,1}$ we can do the "choice" between the two constants $d$ and $e$ as follows:



                                          $$dlambda + e(1-lambda)$$



                                          which equals $d$ for $lambda = 1$, and $e$ for $lambda = 0$.






                                          share|cite|improve this answer










                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.






                                          $endgroup$













                                          • $begingroup$
                                            And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                            $endgroup$
                                            – David Richerby
                                            18 hours ago














                                          1












                                          1








                                          1





                                          $begingroup$

                                          Following solution is not defined for $c = 0$; however it uses very basic operations only, which might be useful as you probably look for an expression to implement in a program:



                                          $$a = b + 1lambda + 2(1-lambda)$$



                                          where



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$





                                          You need to make the problem discrete and make a choice from two values. So, given some value $c in mathbb{R}$ we need to calculate some value $lambda in {0,1}$ depnding on $c<0$ or $c>0$.



                                          Knowing that



                                          $$frac{|c|}{c} in {1,-1}$$



                                          we can calculate the $lambda$ as follows:



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$



                                          Now that our $lambda in {0,1}$ we can do the "choice" between the two constants $d$ and $e$ as follows:



                                          $$dlambda + e(1-lambda)$$



                                          which equals $d$ for $lambda = 1$, and $e$ for $lambda = 0$.






                                          share|cite|improve this answer










                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.






                                          $endgroup$



                                          Following solution is not defined for $c = 0$; however it uses very basic operations only, which might be useful as you probably look for an expression to implement in a program:



                                          $$a = b + 1lambda + 2(1-lambda)$$



                                          where



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$





                                          You need to make the problem discrete and make a choice from two values. So, given some value $c in mathbb{R}$ we need to calculate some value $lambda in {0,1}$ depnding on $c<0$ or $c>0$.



                                          Knowing that



                                          $$frac{|c|}{c} in {1,-1}$$



                                          we can calculate the $lambda$ as follows:



                                          $$lambda = frac{ 1 + frac{|c|}{c} }{2}$$



                                          Now that our $lambda in {0,1}$ we can do the "choice" between the two constants $d$ and $e$ as follows:



                                          $$dlambda + e(1-lambda)$$



                                          which equals $d$ for $lambda = 1$, and $e$ for $lambda = 0$.







                                          share|cite|improve this answer










                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.









                                          share|cite|improve this answer



                                          share|cite|improve this answer








                                          edited yesterday





















                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.









                                          answered yesterday









                                          TimurTimur

                                          1193




                                          1193




                                          New contributor




                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.





                                          New contributor





                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.






                                          Timur is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                                          Check out our Code of Conduct.












                                          • $begingroup$
                                            And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                            $endgroup$
                                            – David Richerby
                                            18 hours ago


















                                          • $begingroup$
                                            And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                            $endgroup$
                                            – David Richerby
                                            18 hours ago
















                                          $begingroup$
                                          And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                          $endgroup$
                                          – David Richerby
                                          18 hours ago




                                          $begingroup$
                                          And you're seriously proposing that I should write all of that instead of "$a=b+1$ if $c>0$ and $a=b+2$, otherwise"? Um...
                                          $endgroup$
                                          – David Richerby
                                          18 hours ago











                                          0












                                          $begingroup$

                                          Fundamentally, the non-answer is the answer. Whatever notation you think you might want to use to express "$a=b+1$ if $c>0$ and $a=b+2$ otherwise" or
                                          $$a=begin{cases}b+1 &text{if }c>0\b+2 &text{otherwise}end{cases}$$
                                          is much harder to read than either of those two things.






                                          share|cite|improve this answer









                                          $endgroup$













                                          • $begingroup$
                                            The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                            $endgroup$
                                            – dataphile
                                            16 hours ago






                                          • 1




                                            $begingroup$
                                            Most of any mathematics paper is natural language. There's a reason for that.
                                            $endgroup$
                                            – David Richerby
                                            15 hours ago
















                                          0












                                          $begingroup$

                                          Fundamentally, the non-answer is the answer. Whatever notation you think you might want to use to express "$a=b+1$ if $c>0$ and $a=b+2$ otherwise" or
                                          $$a=begin{cases}b+1 &text{if }c>0\b+2 &text{otherwise}end{cases}$$
                                          is much harder to read than either of those two things.






                                          share|cite|improve this answer









                                          $endgroup$













                                          • $begingroup$
                                            The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                            $endgroup$
                                            – dataphile
                                            16 hours ago






                                          • 1




                                            $begingroup$
                                            Most of any mathematics paper is natural language. There's a reason for that.
                                            $endgroup$
                                            – David Richerby
                                            15 hours ago














                                          0












                                          0








                                          0





                                          $begingroup$

                                          Fundamentally, the non-answer is the answer. Whatever notation you think you might want to use to express "$a=b+1$ if $c>0$ and $a=b+2$ otherwise" or
                                          $$a=begin{cases}b+1 &text{if }c>0\b+2 &text{otherwise}end{cases}$$
                                          is much harder to read than either of those two things.






                                          share|cite|improve this answer









                                          $endgroup$



                                          Fundamentally, the non-answer is the answer. Whatever notation you think you might want to use to express "$a=b+1$ if $c>0$ and $a=b+2$ otherwise" or
                                          $$a=begin{cases}b+1 &text{if }c>0\b+2 &text{otherwise}end{cases}$$
                                          is much harder to read than either of those two things.







                                          share|cite|improve this answer












                                          share|cite|improve this answer



                                          share|cite|improve this answer










                                          answered 18 hours ago









                                          David RicherbyDavid Richerby

                                          2,18711324




                                          2,18711324












                                          • $begingroup$
                                            The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                            $endgroup$
                                            – dataphile
                                            16 hours ago






                                          • 1




                                            $begingroup$
                                            Most of any mathematics paper is natural language. There's a reason for that.
                                            $endgroup$
                                            – David Richerby
                                            15 hours ago


















                                          • $begingroup$
                                            The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                            $endgroup$
                                            – dataphile
                                            16 hours ago






                                          • 1




                                            $begingroup$
                                            Most of any mathematics paper is natural language. There's a reason for that.
                                            $endgroup$
                                            – David Richerby
                                            15 hours ago
















                                          $begingroup$
                                          The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                          $endgroup$
                                          – dataphile
                                          16 hours ago




                                          $begingroup$
                                          The beauty of formal maths notation is that it expresses identities that can be used to solve / simplify / invert equations without translation to and from a natural language. You are right in a sense, I could just invent a new notation and describe it alongside the equation, but I wouldn't want to reinvent the wheel and risk confusion.
                                          $endgroup$
                                          – dataphile
                                          16 hours ago




                                          1




                                          1




                                          $begingroup$
                                          Most of any mathematics paper is natural language. There's a reason for that.
                                          $endgroup$
                                          – David Richerby
                                          15 hours ago




                                          $begingroup$
                                          Most of any mathematics paper is natural language. There's a reason for that.
                                          $endgroup$
                                          – David Richerby
                                          15 hours ago


















                                          draft saved

                                          draft discarded




















































                                          Thanks for contributing an answer to Mathematics Stack Exchange!


                                          • Please be sure to answer the question. Provide details and share your research!

                                          But avoid



                                          • Asking for help, clarification, or responding to other answers.

                                          • Making statements based on opinion; back them up with references or personal experience.


                                          Use MathJax to format equations. MathJax reference.


                                          To learn more, see our tips on writing great answers.




                                          draft saved


                                          draft discarded














                                          StackExchange.ready(
                                          function () {
                                          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3135798%2fis-there-a-math-expression-equivalent-to-the-conditional-ternary-operator%23new-answer', 'question_page');
                                          }
                                          );

                                          Post as a guest















                                          Required, but never shown





















































                                          Required, but never shown














                                          Required, but never shown












                                          Required, but never shown







                                          Required, but never shown

































                                          Required, but never shown














                                          Required, but never shown












                                          Required, but never shown







                                          Required, but never shown







                                          Popular posts from this blog

                                          Liste der Baudenkmale in Friedland (Mecklenburg)

                                          Single-Malt-Whisky

                                          Czorneboh