Prove f(M,n)=2^(m-1) (2n-1) is an injection and surjection?
Then prove that N x N is equivalent to N and hence that card( N x N) is equal to caleph zero.
- 1 decade agoFavourite answer
This looks messy so I'm not actually going to do it. i'll just give you a little help.
Im going to assume f:R to R (f is a function from the reals to the reals)
To prove that a function is injective you need to prove: for all x,y in R if f(x)=f(y) then x=y
So start with: 2^(m-1)(2n-1)=2^(x-1)(2y-1) and try to reach the conclusion m=x and n=y.
To prove that a function is surjective you need to prove: for all a in R, there exists a b in R such that f(a)=b
So show that 2^(m-1)(2n-1) is in R.