I have already done the proof, but I just want to make sure it is correct!

f: ZxZ -> Z f(m,n)=m+n

Prove that f is onto using the definition of onto.

Proof

Suppose that f(m,n)=m+n.

Let a∈Z.

Then, f(m,n)=a iff m+n=a iff m=a-n which is in Z.

Therefore, f(m+n)=m+n is onto.

Is this correct? Or proper?

Thanks.