Is there such a thing in math the inverse of a sequence?












1












$begingroup$


Such as can I construct a sequence by reversing the order of the approximating sequence of $frac{1}{3}$? So such inverse would look like $left{….,0.333333333,0.3333333,0.333333,...0.3right}$.



I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.










share|cite|improve this question











$endgroup$












  • $begingroup$
    You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
    $endgroup$
    – kingW3
    4 hours ago






  • 1




    $begingroup$
    And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
    $endgroup$
    – астон вілла олоф мэллбэрг
    2 hours ago












  • $begingroup$
    This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
    $endgroup$
    – Somos
    22 mins ago


















1












$begingroup$


Such as can I construct a sequence by reversing the order of the approximating sequence of $frac{1}{3}$? So such inverse would look like $left{….,0.333333333,0.3333333,0.333333,...0.3right}$.



I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.










share|cite|improve this question











$endgroup$












  • $begingroup$
    You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
    $endgroup$
    – kingW3
    4 hours ago






  • 1




    $begingroup$
    And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
    $endgroup$
    – астон вілла олоф мэллбэрг
    2 hours ago












  • $begingroup$
    This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
    $endgroup$
    – Somos
    22 mins ago
















1












1








1





$begingroup$


Such as can I construct a sequence by reversing the order of the approximating sequence of $frac{1}{3}$? So such inverse would look like $left{….,0.333333333,0.3333333,0.333333,...0.3right}$.



I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.










share|cite|improve this question











$endgroup$




Such as can I construct a sequence by reversing the order of the approximating sequence of $frac{1}{3}$? So such inverse would look like $left{….,0.333333333,0.3333333,0.333333,...0.3right}$.



I had this question when I was constructing a sequence that is bounded between 0 and 1/2 and not convergent to 0 for a homework question.







real-analysis sequences-and-series inverse






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 20 mins ago







user917099

















asked 4 hours ago









user917099user917099

1495




1495












  • $begingroup$
    You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
    $endgroup$
    – kingW3
    4 hours ago






  • 1




    $begingroup$
    And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
    $endgroup$
    – астон вілла олоф мэллбэрг
    2 hours ago












  • $begingroup$
    This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
    $endgroup$
    – Somos
    22 mins ago




















  • $begingroup$
    You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
    $endgroup$
    – kingW3
    4 hours ago






  • 1




    $begingroup$
    And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
    $endgroup$
    – астон вілла олоф мэллбэрг
    2 hours ago












  • $begingroup$
    This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
    $endgroup$
    – Somos
    22 mins ago


















$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
4 hours ago




$begingroup$
You can't, imagine if the first element has $n$ three's but in the original sequence the element with $n+1$ three's come after the one with $n$ three's hence in the new sequence it should be before the first element, a contradiction.
$endgroup$
– kingW3
4 hours ago




1




1




$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
2 hours ago






$begingroup$
And no, there is a difference between stupid and bad questions, in your case the votes have matchedvso your question divides opinion. Giving enough context helps when you are asking a "stupid" question, i.e. mentioning that you heard it in class or in conversation with a friend or online on some webpage helps. Also mention what was the broad topic if the conversation, so that others will be able to address concerns relating to that in the answer as well.
$endgroup$
– астон вілла олоф мэллбэрг
2 hours ago














$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
22 mins ago






$begingroup$
This is a good question. In several cases, a sequence makes sense for negative values of the index. For example, the Fibonacci numbers ${0,1,1,2,3,5,dots}$ can be exteneded to negative indices as ${dots,5,-3,2,-1,1}$. I encounter this kind of thing in the OEIS many time.
$endgroup$
– Somos
22 mins ago












1 Answer
1






active

oldest

votes


















7












$begingroup$

A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.



If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.






share|cite|improve this answer











$endgroup$













    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%2f3139613%2fis-there-such-a-thing-in-math-the-inverse-of-a-sequence%23new-answer', 'question_page');
    }
    );

    Post as a guest















    Required, but never shown

























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes









    7












    $begingroup$

    A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.



    If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.






    share|cite|improve this answer











    $endgroup$


















      7












      $begingroup$

      A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.



      If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.






      share|cite|improve this answer











      $endgroup$
















        7












        7








        7





        $begingroup$

        A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.



        If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.






        share|cite|improve this answer











        $endgroup$



        A sequence is ultimately a map whose domain is $mathbb N$, but the object that you describe (a) has no first term, and (b) terminates.



        If you want, I suppose you could define an object whose indices run from $-infty$ to $0$, but that's not appreciably different from looking at the original sequence while standing on your head.







        share|cite|improve this answer














        share|cite|improve this answer



        share|cite|improve this answer








        edited 2 hours ago

























        answered 4 hours ago









        J. MurrayJ. Murray

        53017




        53017






























            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%2f3139613%2fis-there-such-a-thing-in-math-the-inverse-of-a-sequence%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