ThmDex – An index of mathematical definitions, results, and conjectures.
Result R4800 on D15: Set cardinality
Number of injections from a finite set to itself
Formulation 0
Let $n \in \mathbb{N}$ be a D996: Natural number.
Then \begin{equation} |\text{Inj}(\{ 1, \ldots, n \} \to \{ 1, \ldots, n \})| = n! \end{equation}
Proofs
Proof 1
Let $n \in \mathbb{N}$ be a D996: Natural number.
This result is a particular case of R1854: Cardinality of the set of injections between finite sets. $\square$