# Prescription of mapping f: N x N → N which is not injection and surjection

Does exists prescription of mapping f: N x N → N which is not injection and surjection?

• $f((n, t)) = c$ for fixed $c \in \mathbb{N}$ is neither injective nor surjective. There are infinitely many other examples. – dylan7 Oct 2 at 12:09
Let $$f$$ be any constant map. For example $$f:\mathbb{N}\times \mathbb{N} \to \mathbb{N}$$ by $$f((n, m))= k$$ for any $$k \in \mathbb{N}$$ fixed.