Mixing
Are the sets of a power set considered “elements?â€
Clash Royale CLAN TAG#URR8PPP
up vote
3
down vote
favorite
I'm trying to review some set theory. The question I'm encountering is "How many elements are in a power set of a set?" I know the answer if my interpretation of the question is correct. If the original set A has n elements, the power set of A will have 2^n new sets within it, but are these sets considered "elements" of the power set, or am I misinterpreting the question? If these sets are not considered elements of the power set, then is the question asking for the total number of elements of all the sets of the power set? I'm not entirely sure.
elementary-set-theory
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
asked Aug 24 at 1:14
joe_04_04
253110
add a comment |Â
up vote
3
down vote
favorite
I'm trying to review some set theory. The question I'm encountering is "How many elements are in a power set of a set?" I know the answer if my interpretation of the question is correct. If the original set A has n elements, the power set of A will have 2^n new sets within it, but are these sets considered "elements" of the power set, or am I misinterpreting the question? If these sets are not considered elements of the power set, then is the question asking for the total number of elements of all the sets of the power set? I'm not entirely sure.
elementary-set-theory
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
asked Aug 24 at 1:14
joe_04_04
253110
5
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34
add a comment |Â
up vote
3
down vote
favorite
up vote
3
down vote
favorite
I'm trying to review some set theory. The question I'm encountering is "How many elements are in a power set of a set?" I know the answer if my interpretation of the question is correct. If the original set A has n elements, the power set of A will have 2^n new sets within it, but are these sets considered "elements" of the power set, or am I misinterpreting the question? If these sets are not considered elements of the power set, then is the question asking for the total number of elements of all the sets of the power set? I'm not entirely sure.
elementary-set-theory
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
asked Aug 24 at 1:14
joe_04_04
253110
I'm trying to review some set theory. The question I'm encountering is "How many elements are in a power set of a set?" I know the answer if my interpretation of the question is correct. If the original set A has n elements, the power set of A will have 2^n new sets within it, but are these sets considered "elements" of the power set, or am I misinterpreting the question? If these sets are not considered elements of the power set, then is the question asking for the total number of elements of all the sets of the power set? I'm not entirely sure.
elementary-set-theory
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
asked Aug 24 at 1:14
joe_04_04
253110
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
edited Aug 24 at 1:50
Andrés E. Caicedo
63.4k7153238
63.4k7153238
asked Aug 24 at 1:14
joe_04_04
253110
asked Aug 24 at 1:14
joe_04_04
253110
asked Aug 24 at 1:14
joe_04_04
253110
253110
5
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34
add a comment |Â
5
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34
5
5
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
9
down vote
accepted
Short Answer: Yes
Long Answer:
I know why this is confusing, but always think of it this way: a set can contain any kind of objects, but the term elements exclusively refers to the objects that are members of the set. For example, if I say $x$ is an element of $y$, then $xin y$, regardless of what $x$ is, even if it is another set.
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
9
down vote
accepted
Short Answer: Yes
Long Answer:
I know why this is confusing, but always think of it this way: a set can contain any kind of objects, but the term elements exclusively refers to the objects that are members of the set. For example, if I say $x$ is an element of $y$, then $xin y$, regardless of what $x$ is, even if it is another set.
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
add a comment |Â
up vote
9
down vote
accepted
Short Answer: Yes
Long Answer:
I know why this is confusing, but always think of it this way: a set can contain any kind of objects, but the term elements exclusively refers to the objects that are members of the set. For example, if I say $x$ is an element of $y$, then $xin y$, regardless of what $x$ is, even if it is another set.
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
add a comment |Â
up vote
9
down vote
accepted
up vote
9
down vote
accepted
Short Answer: Yes
Long Answer:
I know why this is confusing, but always think of it this way: a set can contain any kind of objects, but the term elements exclusively refers to the objects that are members of the set. For example, if I say $x$ is an element of $y$, then $xin y$, regardless of what $x$ is, even if it is another set.
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
Short Answer: Yes
Long Answer:
I know why this is confusing, but always think of it this way: a set can contain any kind of objects, but the term elements exclusively refers to the objects that are members of the set. For example, if I say $x$ is an element of $y$, then $xin y$, regardless of what $x$ is, even if it is another set.
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
answered Aug 24 at 1:21
Rushabh Mehta
1,718218
1,718218
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
add a comment |Â
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
1
1
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
Also in ZFC (for example), everything is a set anyways
– Ashwin Iyengar
Aug 24 at 1:55
add a comment |Â
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2892694%2fare-the-sets-of-a-power-set-considered-elements%23new-answer', 'question_page');
);
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
5
Each set is an element. In set-builder, $mathcalP(S) = X : X subset S $ where $mathcalP$ is the power set "function."
– Sean Roberson
Aug 24 at 1:17
Should the subset symbol have an underline for possible equality?
– Oscar Lanzi
Aug 24 at 2:00
@OscarLanzi likely a notation difference.
– George V. Williams
Aug 24 at 5:34