===== Bijective function =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $X,Y$ ... set |
| @#FFBB00: definiendum | @#FFBB00: $ f\in \mathrm{Bijective}(X,Y) $ |
| @#AAFFAA: inclusion   | @#AAFFAA: $ f\in \mathrm{Injective}(X,Y) $ |
| @#AAFFAA: inclusion   | @#AAFFAA: $ f\in \mathrm{Surjective}(X,Y) $|

==== Discussion ====
=== Predicates ===
| @#EEEE55: predicate   | @#EEEE55: $X\approx Y\equiv \mathrm{Bijective}(X,Y)\ne\emptyset$ |
We also write $X$ equinumerous $Y$.
| @#EEEE55: predicate   | @#EEEE55: $X\preccurlyeq Y \equiv \exists (X'\subseteq Y).\ X'\approx X$ |
We also write $X$ smaller $Y$.

| @#EEEE55: predicate   | @#EEEE55: $Y$ ... countably infinite $\equiv \mathbb N\approx Y$ |
==== Parents ====
=== Context ===
[[Injective function]], [[Surjective function]]