Inverse of Injection is One-to-One Relation

From ProofWiki
Jump to navigation Jump to search

Theorem

Let $f$ be an injective mapping.


Then its inverse $f^{-1}$ is a one-to-one relation.


Proof

We are given that $f$ is an injective mapping.

Hence by definition $f$ is a one-to-one relation.


The result follows from from Inverse of One-to-One Relation is One-to-One.

$\blacksquare$