Find element in subsets












0














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
























  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 '18 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 '18 at 16:02
















0














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
























  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 '18 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 '18 at 16:02














0












0








0







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















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




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 '18 at 15:58









Servaes

22.4k33793




22.4k33793










asked Nov 20 '18 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 '18 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 '18 at 16:02


















  • Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
    – Servaes
    Nov 20 '18 at 15:58










  • Yes, the sets are disjoint.
    – s__o_
    Nov 20 '18 at 16:02
















Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
– Servaes
Nov 20 '18 at 15:58




Is there a unique such $j$ for every such $e$? That is, are the $S_j$ disjoint?
– Servaes
Nov 20 '18 at 15:58












Yes, the sets are disjoint.
– s__o_
Nov 20 '18 at 16:02




Yes, the sets are disjoint.
– s__o_
Nov 20 '18 at 16:02










1 Answer
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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





















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    1 Answer
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    1 Answer
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    active

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    0














    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


























      0














      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
























        0












        0








        0






        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 '18 at 17:00









        Hagen von Eitzen

        276k21269496




        276k21269496






























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