dimbulb

stupid theorem, and I don't need to be able to prove this, just use its results. but i've been trying to prove this for some time now.

Assume S and T are infinite sets.

if|S|<=|T| and |T|<=|S|, then |S|=|T|

|S| is the cardinality of the set S.

basically, you need to establish a bijection between S and T, while using the fact that there exists an injection from S to T and there exists an injection from T to S.

in plain words, if S is bigger than or equal in size to T, and if T is bigger than or equal in size to S, then S and T are the same size.....

ahhhh.... the mind boggling concept of infinity....