Bijective function

Set

 context $X,Y$ … set definiendum $f\in \mathrm{Bijective}(X,Y)$ inclusion $f\in \mathrm{Injective}(X,Y)$ inclusion $f\in \mathrm{Surjective}(X,Y)$

Discussion

Predicates

 predicate $X\approx Y\equiv \mathrm{Bijective}(X,Y)\ne\emptyset$

We also write $X$ equinumerous $Y$.

 predicate $X\preccurlyeq Y \equiv \exists (X'\subseteq Y).\ X'\approx X$

We also write $X$ smaller $Y$.

 predicate $Y$ … countably infinite $\equiv \mathbb N\approx Y$