Equivalence of Definitions of Bijection/Definition 1 iff Definition 3
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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.
$\blacksquare$