Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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...