ThmDex – An index of mathematical definitions, results, and conjectures.
Result R5093 on D15: Set cardinality
Total number of fixed-length sequences using a given number of labels
Formulation 0
Let $N, M \in \{ 1, 2, 3, \ldots \}$ each be a D5094: Positive integer.
Then \begin{equation} \left| \{ 1, \ldots, M \}^{ \{ 1, \ldots, N \}} \right| = M^N \end{equation}
Proofs
Proof 0
Let $N, M \in \{ 1, 2, 3, \ldots \}$ each be a D5094: Positive integer.
This result is a particular case of R1856: Cardinality of the set of maps between finite sets. $\square$