# Power set?

1. Dec 6, 2014

### HMPARTICLE

1. The problem statement, all variables and given/known data

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

Last edited by a moderator: Dec 7, 2014
2. Dec 6, 2014

### Staff: Mentor

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

3. Dec 7, 2014

### HMPARTICLE

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! :(.

4. Dec 7, 2014

### pasmith

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

5. Dec 7, 2014

### 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.