Editing Binary function (section)

==Generalisations==
The various concepts relating to functions can also be generalised to binary functions.
For example, the division example above is ''[[surjective function|surjective]]'' (or ''onto'') because every rational number may be expressed as a quotient of an integer and a natural number.
This example is ''[[injective function|injective]]'' in each input separately, because the functions ''f'' <sup>''x''</sup> and ''f'' <sub>''y''</sub> are always injective.
However, it's not injective in both variables simultaneously, because (for example) ''f'' (2,4) = ''f'' (1,2).

One can also consider ''partial'' binary functions, which may be defined only for certain values of the inputs.
For example, the division example above may also be interpreted as a partial binary function from '''Z''' and '''N''' to '''Q''', where '''N''' is the set of all natural numbers, including zero.
But this function is undefined when the second input is zero.

A [[binary operation]] is a binary function where the sets ''X'', ''Y'', and ''Z'' are all equal; binary operations are often used to define [[algebraic structure]]s.

In [[linear algebra]], a [[bilinear operator|bilinear transformation]] is a binary function where the sets ''X'', ''Y'', and ''Z'' are all [[vector space]]s and the derived functions ''f'' <sup>''x''</sup> and ''f''<sub>''y''</sub> are all [[linear transformation]]s.
A bilinear transformation, like any binary function, can be interpreted as a function from ''X'' × ''Y'' to ''Z'', but this function in general won't be linear.
However, the bilinear transformation can also be interpreted as a single linear transformation from the [[tensor product]] <math>X \otimes Y</math> to ''Z''.