[SOLVED] nonempty set, injective function

Prove or disprove: For every nonempty set A, there exists an injective function f: A -> P(A).
So this is saying that for this function f, every element of A has an image in the power set of A, right? But not every element of the power set has to be defined by f(A), right?
I think this could be proven but honestly i cannot think of a way to go about doing it. Please help and if you have a strategy please explain where you got it/how you came up with it so I can better understand the problem. Thanks so much!

Hello deathbyproofs

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Originally Posted by deathbyproofs

Prove or disprove: For every nonempty set A, there exists an injective function f: A -> P(A).
So this is saying that for this function f, every element of A has an image in the power set of A, right? But not every element of the power set has to be defined by f(A), right?

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Yes, you are quite right. So if we're going to prove the statement, all we need to do is to find a function that does this.

Well, the power set is the set of all the subsets of . So, for any . Therefore if we define as , that would do it.

Grandad