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anonymous
 4 years ago
My book on Sets says:
If A is a set, then P(A) = { X: X ⊆ A} is called the power set. It is the set of all subsets of A.
However the definition seems to say, every in P(A) is a subset of A, but they may be the same subset. Basically, the second sentence of the definition does not ring true to me.
anonymous
 4 years ago
My book on Sets says: If A is a set, then P(A) = { X: X ⊆ A} is called the power set. It is the set of all subsets of A. However the definition seems to say, every in P(A) is a subset of A, but they may be the same subset. Basically, the second sentence of the definition does not ring true to me.

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Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1I'm not following what you problem is with this definition

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0It says, it is the set of all subsets of A. However, I don't see where 'all' comes from.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ie. all possibilities of subsets of a set

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1yes..that is what is is...the set of all subsets of a given set.. P(A) = { X: X ⊆ A} is read as the set of all sets X such that X is a subset of A

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Ok so it's implicitly stated because of P?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1sure P(A) = { X: X ⊆ A} and the set of all subsets of A. are two ways to say the exact same thing.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0What does B = {X : X ⊆ A} mean?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1it says that B is the powerset :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0But couldn't this mean say A is {1,2,3} that B = {{1},{1},{1}} since it's true that all elements are subsets?

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1if A={1,2,3} and B=P(A) then \[B=\{\emptyset,\{1\},\{2\},\{3\},\{1,2\},\{1,3\},\{2,3\},\{1,2,3\}\}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0but the notation is different. B = {X : X ⊆ A} is not B=P(A).How would one define the rules for the previous example? Like A = {1,2,3} then B ={{1},{1},{1}} or B could be {{1},{2},{2}} etc as long as the elements were subsets. Thanks!

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1if \[B=\{XX\subseteq A\}\] then B is the same as P(A)

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1also you should stop writing B ={{1},{1},{1}} because it make sense. you don't have repeated elements in a set.

Zarkon
 4 years ago
Best ResponseYou've already chosen the best response.1*because it make no sense

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0ah yeah of course. Thanks for clearing things up. :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I'll be sure to ask more questions later
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