Set theory notation for intersection
$begingroup$
I've started reading Probability by Blikzstein and Wang and run into the following formula:
$B = bigcap_{j=1}^{10} A_{j}$
I wasn't able to find a definition of the notation in the book, or on Wikipedia:
- https://en.wikipedia.org/wiki/Set_notation
- https://en.wikipedia.org/wiki/Set-builder_notation
- https://en.wikipedia.org/wiki/Set_theory
I think I can guess what the notation means, but I was hoping to find a formal definition.
I have seen a similar question here: Set Theory Notation Crises, however that question does not have the digits above the intersection symbol.
elementary-set-theory notation
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
$endgroup$
add a comment |
$begingroup$
I've started reading Probability by Blikzstein and Wang and run into the following formula:
$B = bigcap_{j=1}^{10} A_{j}$
I wasn't able to find a definition of the notation in the book, or on Wikipedia:
- https://en.wikipedia.org/wiki/Set_notation
- https://en.wikipedia.org/wiki/Set-builder_notation
- https://en.wikipedia.org/wiki/Set_theory
I think I can guess what the notation means, but I was hoping to find a formal definition.
I have seen a similar question here: Set Theory Notation Crises, however that question does not have the digits above the intersection symbol.
elementary-set-theory notation
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
$endgroup$
add a comment |
$begingroup$
I've started reading Probability by Blikzstein and Wang and run into the following formula:
$B = bigcap_{j=1}^{10} A_{j}$
I wasn't able to find a definition of the notation in the book, or on Wikipedia:
- https://en.wikipedia.org/wiki/Set_notation
- https://en.wikipedia.org/wiki/Set-builder_notation
- https://en.wikipedia.org/wiki/Set_theory
I think I can guess what the notation means, but I was hoping to find a formal definition.
I have seen a similar question here: Set Theory Notation Crises, however that question does not have the digits above the intersection symbol.
elementary-set-theory notation
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
$endgroup$
I've started reading Probability by Blikzstein and Wang and run into the following formula:
$B = bigcap_{j=1}^{10} A_{j}$
I wasn't able to find a definition of the notation in the book, or on Wikipedia:
- https://en.wikipedia.org/wiki/Set_notation
- https://en.wikipedia.org/wiki/Set-builder_notation
- https://en.wikipedia.org/wiki/Set_theory
I think I can guess what the notation means, but I was hoping to find a formal definition.
I have seen a similar question here: Set Theory Notation Crises, however that question does not have the digits above the intersection symbol.
elementary-set-theory notation
elementary-set-theory notation
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
edited Jan 8 at 12:19
Asaf Karagila♦
302k32427758
302k32427758
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
asked Jan 8 at 12:15
Chris SnowChris Snow
1607
1607
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
In set theory given a class term $X$ its intersection is defined as
$$
bigcap X := {x mid forall y in X, x in y}.
$$
Now, note that we can equivalently write
$$
bigcap_{j = 1}^{10} A_j = bigcap {A_j mid forall j in {1, ldots, 10}}.
$$
Therefore
$$
bigcap_{j = 1}^{10} A_j = {x mid forall j in {1, ldots, 10}, x in A_j}.
$$
Check out 'Introduction to set theory' by Hrbacek and Jech for further info.
answered Jan 8 at 14:23
Random N.Random N.
362
$endgroup$
add a comment |
$begingroup$
It's a short-hand notation for $B= A_1cap A_2cap ldots cap A_{10}$.
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In set theory given a class term $X$ its intersection is defined as
$$
bigcap X := {x mid forall y in X, x in y}.
$$
Now, note that we can equivalently write
$$
bigcap_{j = 1}^{10} A_j = bigcap {A_j mid forall j in {1, ldots, 10}}.
$$
Therefore
$$
bigcap_{j = 1}^{10} A_j = {x mid forall j in {1, ldots, 10}, x in A_j}.
$$
Check out 'Introduction to set theory' by Hrbacek and Jech for further info.
answered Jan 8 at 14:23
Random N.Random N.
362
$endgroup$
add a comment |
$begingroup$
In set theory given a class term $X$ its intersection is defined as
$$
bigcap X := {x mid forall y in X, x in y}.
$$
Now, note that we can equivalently write
$$
bigcap_{j = 1}^{10} A_j = bigcap {A_j mid forall j in {1, ldots, 10}}.
$$
Therefore
$$
bigcap_{j = 1}^{10} A_j = {x mid forall j in {1, ldots, 10}, x in A_j}.
$$
Check out 'Introduction to set theory' by Hrbacek and Jech for further info.
answered Jan 8 at 14:23
Random N.Random N.
362
$endgroup$
add a comment |
$begingroup$
In set theory given a class term $X$ its intersection is defined as
$$
bigcap X := {x mid forall y in X, x in y}.
$$
Now, note that we can equivalently write
$$
bigcap_{j = 1}^{10} A_j = bigcap {A_j mid forall j in {1, ldots, 10}}.
$$
Therefore
$$
bigcap_{j = 1}^{10} A_j = {x mid forall j in {1, ldots, 10}, x in A_j}.
$$
Check out 'Introduction to set theory' by Hrbacek and Jech for further info.
answered Jan 8 at 14:23
Random N.Random N.
362
$endgroup$
In set theory given a class term $X$ its intersection is defined as
$$
bigcap X := {x mid forall y in X, x in y}.
$$
Now, note that we can equivalently write
$$
bigcap_{j = 1}^{10} A_j = bigcap {A_j mid forall j in {1, ldots, 10}}.
$$
Therefore
$$
bigcap_{j = 1}^{10} A_j = {x mid forall j in {1, ldots, 10}, x in A_j}.
$$
Check out 'Introduction to set theory' by Hrbacek and Jech for further info.
answered Jan 8 at 14:23
Random N.Random N.
362
answered Jan 8 at 14:23
Random N.Random N.
362
answered Jan 8 at 14:23
Random N.Random N.
362
answered Jan 8 at 14:23
Random N.Random N.
362
362
add a comment |
add a comment |
$begingroup$
It's a short-hand notation for $B= A_1cap A_2cap ldots cap A_{10}$.
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
$endgroup$
add a comment |
$begingroup$
It's a short-hand notation for $B= A_1cap A_2cap ldots cap A_{10}$.
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
$endgroup$
add a comment |
$begingroup$
It's a short-hand notation for $B= A_1cap A_2cap ldots cap A_{10}$.
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
$endgroup$
It's a short-hand notation for $B= A_1cap A_2cap ldots cap A_{10}$.
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
answered Jan 8 at 12:17
WuestenfuxWuestenfux
3,9951411
3,9951411
add a comment |
add a comment |
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