Let $n, m \in \mathbb{N}$ each be a D996: Natural number such that
| (i) | $\text{Inj}(\{ 1, \ldots, n \} \to \{ 1, \ldots, m \})$ is the D2222: Set of injections from $\{ 1, \ldots, n \}$ to $\{ 1, \ldots, m \}$ |
Then
| (1) | \begin{equation} m > n \quad \implies \quad |\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})| = 0 \end{equation} |
| (2) | \begin{equation} m \leq n \quad \implies \quad |\text{Inj}(\{ 1, \ldots, m \} \to \{ 1, \ldots, n \})| = \frac{n !}{(n - m) !} \end{equation} |