Size of the Power Set


by michonamona
Tags: power, size
michonamona
michonamona is offline
#1
Feb17-11, 08:22 PM
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
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Robert1986
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#2
Feb17-11, 08:45 PM
P: 828
Quote Quote by michonamona View Post
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.
LCKurtz
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#3
Feb17-11, 10:42 PM
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Quote Quote by michonamona View Post
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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