# Size of the Power Set

by michonamona
Tags: power, size
 P: 122 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
P: 828
 Quote by michonamona 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
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.
HW Helper
Thanks
PF Gold
P: 7,659
 Quote by michonamona 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
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.

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