Prove the power set of X exists

[HMPARTICLE]

Homework Statement

Let X be a set. Then the set

{Y:Y is a subset of X}

prove this is a set.Where do i start?

Really unsure, i know that i have to use the power set?

I have written down;

{0,1}^X

 

[jedishrfu]

What techniques have you learned so far? And what level of math is this for?

 

[HMPARTICLE]

undergraduate analysis.
I know how to prove basic things, like umm.
If f and g are both injective then so is g composed with f etc.
i want to say that it is a collection of unordered objects and is therefore a set. (Waste of words, i know)

It just seems WAY to abstract, the fact that {Y: Y is a subset of X} is a set of subsets of a set, surely proves that it is in fact a set! :(.

 

[pasmith]

What formal definition of "set" are you told to use?

 

[HMPARTICLE]

there is no formal definition, there is an informal definition that says that:

We define a set A to be any unordered collection of objects.