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Say I make a function $f$ that takes a parameter $a$, but I want to make sure that $a$ can only be $\mathbb{N}$, no $\mathbb{Z}$ or $\mathbb{R}$ allowed (as an example), how would I write that in a clear and concise way?

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$f\colon \mathbb{N} \to X$. – Daniel Fischer Jul 17 '13 at 19:28
up vote 4 down vote accepted

Let $f$ be a function whose domain is $\Bbb N$.

Let $a\in \Bbb N$ and define $f(a)=\cdots$.

Let $f\colon \Bbb N\to X$ be a function, for some set $X$.

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