# Sets of Permutations of Equivalent Sets are Equivalent

Jump to navigation
Jump to search

## Theorem

Let $A$ and $B$ be sets such that:

- $A \sim B$

where $\sim$ denotes set equivalence.

Let $\map \Gamma A$ denote the set of permutations on $A$.
Then:

- $\map \Gamma A \sim \map \Gamma B$

## Proof

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): Chapter $3$. Mappings: Exercise $12$