Example · High school
Terms
| Term | This example | Why |
|---|
| injective |
✓ |
$x \mapsto 2x$ is injective because it is bijective.
|
| surjective |
✓ |
$x \mapsto 2x$ is surjective because it is bijective.
|
| bijective |
✓ |
$x \mapsto 2x$ is bijective because it has inverse $x \mapsto x / 2$
|
| endomorphism |
✓ |
$x \mapsto 2x$ is a linear map from $\reals$ to itself, so it is an endomorphism.
|
| automorphism |
✓ |
$x \mapsto 2x$ is an automorphism on $\reals$$ because it is a linear map $\reals \to \reals$ and is bijective.
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