Let $\mathbb{N}$ be the D225: Set of natural numbers.
A D11: Set $X$ is a countable set if and only if \begin{equation} \exists \, E \subseteq \mathbb{N} : \text{Bij}(E \to X) \neq \emptyset \end{equation}

Let $\mathbb{N}$ be the D225: Set of natural numbers.
A D11: Set $X$ is a countable set if and only if there exists a D18: Map $f : E \to X$ such that

(1)	$E \subseteq \mathbb{N}$ is a D78: Subset of $\mathbb{N}$
(2)	$f$ is a D468: Bijective map from $E$ to $X$