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The topic we were covering was set theory, and as I had been studying very basic combinatorics the night before, I noticed something about the powerset, namely:

Assuming a set S with n elements:

|P(S)|=2^n

however, if S has n elements, and the powerset is compose of S's subsets, then:

|P(S)|= C(n,0)+C(n,1)...+C(n,n)

so

C(n,0)+C(n,1)...+C(n,n)=2^n

so

[tex]\sum^{n}_{i=0}(\stackrel{n}{i})=2^n[/tex]

I asked about this after class, and he said the binomial theorem could be derived through this identity, I sort of see how, but I doubt the corectness of these ways. Does anybody know about a way to go about this?