Inverse of Injection is One-to-One Relation

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.

$\blacksquare$


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): one-to-one function (one-to-one mapping, one-to-one map)
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