ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Bijective map
Set automorphism
Permutation
Definition D6186
Standard permutation
Formulation 0
Let $N \in \{ 1, 2, 3, \ldots \}$ be a D5094: Positive integer such that
(i) $f : \{ 1, \ldots, N \} \to \{ 1, \ldots, N \}$ is a D5406: Positive integer function on $\{ 1, \ldots, N \}$
Then $f$ is a standard permutation with respect to $N$ if and only if $f$ is a D468: Bijective map.