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Proposition: Characterization of Bijective Functions
Let $f:A\to B$ be a function $f$ is bijective if and only if there is a unique function $g:B\to A$ such that:
* its composition with $f$ is the identity function on $A$, formally $g\circ f=id_A$, and
* $f$'s composition with $g$ is the identity function on $B$, formally $f\circ g=id_B.$
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References
Bibliography
- Modler, F.; Kreh, M.: "Tutorium Analysis 1 und Lineare Algebra 1", Springer Spektrum, 2018, 4th Edition
