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

Could you please help me with that? Thank you

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  • $\begingroup$ $f((n, t)) = c$ for fixed $c \in \mathbb{N} $ is neither injective nor surjective. There are infinitely many other examples. $\endgroup$ – dylan7 Oct 2 at 12:09
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    $\begingroup$ What is a prescription of mapping?! The map f(a,b)=a+1 is neither injective nor surjective. f(1,1)=f(1,2), so f is not injective. 0 is not in the image of f, so f is not surjective. $\endgroup$ – Mircea Oct 2 at 12:12
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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.

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