Find element in subsets











up vote
0
down vote

favorite












I'm quite new to the field of set theory.
I have $n$ sets, so that $S_1 cup S_2 cup ... cup S_n = bigcup_{j=1}^n S_j$.
Now, I would like to find the subset $s_j$ that contains some element $e in S_j$. In other words, I would like to get the index of the $j$'th subset, that contains $e$. Is this even possible to express?



I have the feeling, that my problem might be connected to this: subset of element but I don't get my head around it.



Thank you.










share|cite|improve this question
























  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 at 16:02















up vote
0
down vote

favorite












I'm quite new to the field of set theory.
I have $n$ sets, so that $S_1 cup S_2 cup ... cup S_n = bigcup_{j=1}^n S_j$.
Now, I would like to find the subset $s_j$ that contains some element $e in S_j$. In other words, I would like to get the index of the $j$'th subset, that contains $e$. Is this even possible to express?



I have the feeling, that my problem might be connected to this: subset of element but I don't get my head around it.



Thank you.










share|cite|improve this question
























  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 at 16:02













up vote
0
down vote

favorite









up vote
0
down vote

favorite











I'm quite new to the field of set theory.
I have $n$ sets, so that $S_1 cup S_2 cup ... cup S_n = bigcup_{j=1}^n S_j$.
Now, I would like to find the subset $s_j$ that contains some element $e in S_j$. In other words, I would like to get the index of the $j$'th subset, that contains $e$. Is this even possible to express?



I have the feeling, that my problem might be connected to this: subset of element but I don't get my head around it.



Thank you.










share|cite|improve this question















I'm quite new to the field of set theory.
I have $n$ sets, so that $S_1 cup S_2 cup ... cup S_n = bigcup_{j=1}^n S_j$.
Now, I would like to find the subset $s_j$ that contains some element $e in S_j$. In other words, I would like to get the index of the $j$'th subset, that contains $e$. Is this even possible to express?



I have the feeling, that my problem might be connected to this: subset of element but I don't get my head around it.



Thank you.







elementary-set-theory






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 20 at 15:58









Servaes

21.8k33792




21.8k33792










asked Nov 20 at 15:37









s__o_

1




1












  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 at 16:02


















  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 at 16:02
















Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
– Servaes
Nov 20 at 15:58




Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
– Servaes
Nov 20 at 15:58












Yes, the sets are disjoint.
– s__o_
Nov 20 at 16:02




Yes, the sets are disjoint.
– s__o_
Nov 20 at 16:02










1 Answer
1






active

oldest

votes

















up vote
0
down vote













Given $e$,
$${,iinBbb Nmid ein S_i,} $$
is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
$$bigcup {,iinBbb Nmid ein S_i,}.$$






share|cite|improve this answer





















    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',
    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%2f3006469%2ffind-element-in-subsets%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








    up vote
    0
    down vote













    Given $e$,
    $${,iinBbb Nmid ein S_i,} $$
    is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
    $$bigcup {,iinBbb Nmid ein S_i,}.$$






    share|cite|improve this answer

























      up vote
      0
      down vote













      Given $e$,
      $${,iinBbb Nmid ein S_i,} $$
      is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
      $$bigcup {,iinBbb Nmid ein S_i,}.$$






      share|cite|improve this answer























        up vote
        0
        down vote










        up vote
        0
        down vote









        Given $e$,
        $${,iinBbb Nmid ein S_i,} $$
        is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
        $$bigcup {,iinBbb Nmid ein S_i,}.$$






        share|cite|improve this answer












        Given $e$,
        $${,iinBbb Nmid ein S_i,} $$
        is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
        $$bigcup {,iinBbb Nmid ein S_i,}.$$







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Nov 20 at 17:00









        Hagen von Eitzen

        275k21267494




        275k21267494






























            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.





            Some of your past answers have not been well-received, and you're in danger of being blocked from answering.


            Please pay close attention to the following guidance:


            • 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.


            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%2f3006469%2ffind-element-in-subsets%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

            Ellipse (mathématiques)

            Quarter-circle Tiles

            Mont Emei