Concept# Binary function

Summary

In mathematics, a binary function (also called bivariate function, or function of two variables) is a function that takes two inputs.
Precisely stated, a function f is binary if there exists sets X, Y, Z such that
:,f \colon X \times Y \rightarrow Z
where X \times Y is the Cartesian product of X and Y.
Alternative definitions
Set-theoretically, a binary function can be represented as a subset of the Cartesian product X \times Y \times Z, where (x,y,z) belongs to the subset if and only if f(x,y) = z.
Conversely, a subset R defines a binary function if and only if for any x \in X and y \in Y, there exists a unique z \in Z such that (x,y,z) belongs to R.
f(x,y) is then defined to be this z.
Alternatively, a binary function may be interpreted as simply a fu

Official source

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