Prove that .
I know of a fact that . The problem here is how I can go about establishing the bijective function non-trivially.
Thanks in advance.
Note, this extends to show that .
If S and T are 1-1, then B^S and B^T are 1-1.
I would just prove that more general result.
Or are you asking how to prove that N and NxN are 1-1?
Do you have the fundamental theorem of arithmetic at your disposal? If so, it's easy to get an injection form NxN into N. If not, then there are other ways too.