Size of the Power Set

  1. Feb 17, 2011 #1
    1. The problem statement, all variables and given/known data



    Why is the size of the power set 2^n ?

    To elaborate, suppose we have a set B that has n elements. Let C be the set that contains all the possible subset of B. Why is it that |C|=2^n ?

    It boggles my mind why the base is 2 for all size of sets.

    Thank you,

    M

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 17, 2011 #2
    Haha, keep doing combinatorics and a lot of stuff will blow your mind.


    I don't want to give too much away, here, I'll be around to help if you need it, but think about the set and the power set of that set as a binary string of length n where each element of the string represents an element of the set.
     
  4. Feb 17, 2011 #3

    LCKurtz

    User Avatar
    Homework Helper
    Gold Member

    If you have a set with n elements, now many subsets of size 0 are there? Of size 1? Size 2?...Size n? How many total then?

    Then think about the binomial expansion of (1+1)n.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Similar Discussions: Size of the Power Set
  1. Power Sets (Replies: 4)

  2. The Power Set (Replies: 1)

  3. Power set (Replies: 2)

  4. Power set? (Replies: 4)

Loading...