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Power set?

  1. Dec 6, 2014 #1
    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. jcsd
  3. Dec 6, 2014 #2

    jedishrfu

    Staff: Mentor

    What techniques have you learned so far? And what level of math is this for?
     
  4. Dec 7, 2014 #3
    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! :(.
     
  5. Dec 7, 2014 #4

    pasmith

    User Avatar
    Homework Helper

    What formal definition of "set" are you told to use?
     
  6. Dec 7, 2014 #5
    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.
     
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