Hey guys, I just learned about combinatorical style proofs. Anyways, I was wondering if you could just tell me if the following proof of mine is acceptable.

Claim:

+

+...+

=

Proof. The left hand side and the right hand side count the number of subsets of an n element set. We need to show that the RHS is equilivent to the LHS. We do this as follows. Take an arbitrary subset of the n element set. We need to determine whether or not each element of the n set is in this subset. This gives us

2x2x2x...x2=

possibilities. Hence, RHS=LHS.