= Solution
A <set> $A$ is a <countable set> if there exists an <injective function> $A\to\mathbb N$, with $\mathbb N=\{0,1,2,\ldots\}$. Equivalently, it is a <finite set> or has a <bijection> with $\mathbb N$. An infinite <countable set> is called a <countably infinite set>.
The empty <set> is included: the empty <function> into $\mathbb N$ is injective. This convention distinguishes “countable” from “countably infinite” and will also cover the finite threshold <sets> in the last part.
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