Identity Mapping is Permutation

Theorem

The identity mapping $I_S: S \to S$ on the set $S$ is a permutation.


Proof

The identity mapping $I_S$ is a bijection from $S$ to itself, by Identity Mapping is Bijection.

$\blacksquare$


Sources

  • 1965: J.A. Green: Sets and Groups ... (previous) ... (next): $\S 3.6$. Products of bijective mappings. Permutations
  • 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 7$: Semigroups and Groups: Example $7.5$
  • 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 24.2$: Composition of Mappings
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