Mixing
How to I define the following in set builder notation?
$begingroup$
Let A, B be sets. Sharon defines A % B to be the set of all subsets of A that also contain at least one element in B.
elementary-set-theory
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
$endgroup$
add a comment |
$begingroup$
Let A, B be sets. Sharon defines A % B to be the set of all subsets of A that also contain at least one element in B.
elementary-set-theory
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
$endgroup$
add a comment |
$begingroup$
Let A, B be sets. Sharon defines A % B to be the set of all subsets of A that also contain at least one element in B.
elementary-set-theory
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
$endgroup$
Let A, B be sets. Sharon defines A % B to be the set of all subsets of A that also contain at least one element in B.
elementary-set-theory
elementary-set-theory
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
edited Feb 3 at 3:17
Andrés E. Caicedo
66k8160252
66k8160252
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
asked Feb 3 at 2:55
Sunita JainSunita Jain
182
182
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
$A%B={ xin P(A)mid xcap Bneqemptyset}$, where $P(A)$ is the set of subsets of $A$ (the so-called "power set").
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
$endgroup$
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
add a comment |
$begingroup$
${C: Csubset Aland Ccap Bne emptyset}$....OR
${Csubset A: Ccap Bne emptyset}.$
I prefer the colon $;:;$ to the vertical line $;|;$ because the vertical line has several other uses in math.
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
$endgroup$
add a comment |
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2 Answers
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2 Answers
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$begingroup$
$A%B={ xin P(A)mid xcap Bneqemptyset}$, where $P(A)$ is the set of subsets of $A$ (the so-called "power set").
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
$endgroup$
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
add a comment |
$begingroup$
$A%B={ xin P(A)mid xcap Bneqemptyset}$, where $P(A)$ is the set of subsets of $A$ (the so-called "power set").
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
$endgroup$
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
add a comment |
$begingroup$
$A%B={ xin P(A)mid xcap Bneqemptyset}$, where $P(A)$ is the set of subsets of $A$ (the so-called "power set").
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
$endgroup$
$A%B={ xin P(A)mid xcap Bneqemptyset}$, where $P(A)$ is the set of subsets of $A$ (the so-called "power set").
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
edited Feb 4 at 19:00
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
answered Feb 3 at 3:04
Chris CusterChris Custer
14.4k3827
14.4k3827
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
add a comment |
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
$begingroup$
Fine. For technical reasons it would probably be better to write ${ xin P(A)mid xcap Bneqemptyset}$. See the remarks on the badness of "unrestricted comprehension" at en.wikipedia.org/wiki/Axiom_schema_of_specification .
$endgroup$
– David C. Ullrich
Feb 4 at 13:16
add a comment |
$begingroup$
${C: Csubset Aland Ccap Bne emptyset}$....OR
${Csubset A: Ccap Bne emptyset}.$
I prefer the colon $;:;$ to the vertical line $;|;$ because the vertical line has several other uses in math.
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
$endgroup$
add a comment |
$begingroup$
${C: Csubset Aland Ccap Bne emptyset}$....OR
${Csubset A: Ccap Bne emptyset}.$
I prefer the colon $;:;$ to the vertical line $;|;$ because the vertical line has several other uses in math.
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
$endgroup$
add a comment |
$begingroup$
${C: Csubset Aland Ccap Bne emptyset}$....OR
${Csubset A: Ccap Bne emptyset}.$
I prefer the colon $;:;$ to the vertical line $;|;$ because the vertical line has several other uses in math.
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
$endgroup$
${C: Csubset Aland Ccap Bne emptyset}$....OR
${Csubset A: Ccap Bne emptyset}.$
I prefer the colon $;:;$ to the vertical line $;|;$ because the vertical line has several other uses in math.
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
answered Feb 3 at 3:06
DanielWainfleetDanielWainfleet
35.9k31648
35.9k31648
add a comment |
add a comment |
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