Let $\lambda \in (0, \infty)$ be a D5407: Positive real number such that

(i)	$\text{Binomial}(N, \lambda / N)$ is a D208: Binomial random natural number for each $N \in \{ 1, 2, 3, \, \ldots \}$

A D5216: Random natural number $X \in \text{Random}(\mathbb{N})$ is a Poisson random natural number with parameter $\lambda$ if and only if \begin{equation} X \overset{d}{=} \lim_{N \to \infty} \text{Binomial}(N, \lambda / N) \end{equation}