Mixing
Find element in subsets
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
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
1
add a comment |
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
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
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
add a comment |
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
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
1
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
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
1
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
1
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
edited Nov 20 '18 at 15:58
Servaes
22.4k33793
22.4k33793
asked Nov 20 '18 at 15:37
s__o_
1
asked Nov 20 '18 at 15:37
s__o_
1
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
add a comment |
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
add a comment |
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
$$bigcup {,iinBbb Nmid ein S_i,}.$$
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
add a comment |
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1 Answer
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votes
Given $e$,
$${,iinBbb Nmid ein S_i,} $$
is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
$$bigcup {,iinBbb Nmid ein S_i,}.$$
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
add a comment |
Given $e$,
$${,iinBbb Nmid ein S_i,} $$
is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
$$bigcup {,iinBbb Nmid ein S_i,}.$$
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
add a comment |
Given $e$,
$${,iinBbb Nmid ein S_i,} $$
is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
$$bigcup {,iinBbb Nmid ein S_i,}.$$
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
Given $e$,
$${,iinBbb Nmid ein S_i,} $$
is ${j}$ if $ein S_j$. To ontain $j$ itself, we can use
$$bigcup {,iinBbb Nmid ein S_i,}.$$
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
answered Nov 20 '18 at 17:00
Hagen von Eitzen
276k21269496
276k21269496
add a comment |
add a comment |
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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