Re: Question: Given |X|>0 and |Y|>0, can X x Y be empty?

On Aug 8, 5:12 pm, Scott <ToaTe...@xxxxxxxxx> wrote:
If I look at the Cantor's Proof (pg 158 in [1]), no where does it say
given a function f:S->P(S) there is a set A_f in P(S) that is not in
the range of f.

Well, we can't see your book, but just for future reference:
Cantor's theorem says EXACTLY that. It says that
given a function on S into P(S), the function is not also Onto P(S),
i.e., there is an element of P(S) -- a subset of S -- that is NOT
f(s) for any s in S, i.e., that is not in the range of f.
THAT IS
the theorem. ANY proof of the theorem basically says that
AT THE END, AS its CONCLUSION. If you are not going to
post your lame textbook then you should expect people to be
contemptuous. If you do post it then they will just point out how
you couldn't even read it.

.