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Injective function
Set
$X,Y$ |
$ f\in \mathrm{Injective}(X,Y)$ |
$ f:X\to Y $ |
$ f(x)=f(y) \implies x=y $ |
Discussion
Predicates
$Y$ …countably infinite $\equiv (\mathrm{Injective}(\mathbb N,Y)\ne\emptyset) $ |
$Y$ … countable $\equiv$ ($Y$ …finite) $\lor$ ($Y$ …countably infinite) |