Definition:Reverse Bijections

Definition
Let $S$ and $T$ be sets.

Let:
 * $f : S \to T$
 * $g : T \to S$

be mappings.

Then $f$ and $g$ are reverse bijections both:
 * $f \circ g = \operatorname{id}_T$
 * $g \circ f = \operatorname{id}_S$

where:
 * $\circ$ denotes composition of mappings
 * $\operatorname{id}$ denotes the identity mapping on a set.

Also see

 * Definition:Bijection
 * Definition:Inverse Mapping