| 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) $ |
| 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 $\equiv \mathbb N\approx Y$ |