# Equivalence of Definitions of Bijection/Definition 1 iff Definition 3

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## Contents

## Theorem

The following definitions of the concept of **Bijection** are equivalent:

### Definition 1

A mapping $f: S \to T$ is a **bijection** if and only if both:

- $(1): \quad f$ is an injection

and:

- $(2): \quad f$ is a surjection.

### Definition 3

A mapping $f: S \to T$ is a **bijection** if and only if:

## Proof

This is demonstrated in Mapping is Injection and Surjection iff Inverse is Mapping.

$\blacksquare$