Here's an opportunity for you to give another proof of the fact that

N\\\\times N

is countably infinite. Define

g:N\\\\times N->N

by\

g(m,n)=2^(m-1)(2n-1)

\ and use the Fundamental Theorem of Arithmetic to show that

g

is a bijection.

Here's an opportunity for you to give another proof of the fact that NN is countably infinite. Define g:NNN by g(m,n)=2m1(2n1) and use the Fundamental Theorem of Arithmetic to show that g is a bijection