# Two-Input Function

A two-input function is a formal function with two function arguments.

**AKA:**Binary Function.**Example(s):**- [math]\displaystyle{ f(x,y) = 2x \times \sqrt{y} }[/math]

**Counter-Example(s):**- a Two Value-Output Function (that does not have Two Function Arguments).
- Unary Function.
- Ternary Function, such as a Binomial Probability Mass Function.
- n-Ary Function.

**See:**Binary Set Operation.

## References

### 2011

- http://en.wikipedia.org/wiki/Binary_function
- In mathematics, a
**binary function**, or function of two variables, is a function which takes two inputs.Precisely stated, a function [math]\displaystyle{ f }[/math] is binary if there exists sets [math]\displaystyle{ X, Y, Z }[/math] such that [math]\displaystyle{ \,f \colon X \times Y \rightarrow Z }[/math] where [math]\displaystyle{ X \times Y }[/math] is the Cartesian product of [math]\displaystyle{ X }[/math] and [math]\displaystyle{ Y. }[/math]

For example, if

**Z**is the set of integers,**N**^{+}is the set of natural numbers (except for zero), and**Q**is the set of rational numbers, then division is a binary function from**Z**and NQ.^{+}toSet-theoretically, one may represent a binary function as a subset of the Cartesian product

*X*× Y*×*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*. We then define*f*(*x*,*y*) to be this*z*.**Alternatively, a binary function may be interpreted as simply a function from*X ×*Y*to*Z*.Even when thought of this way, however, one generally writes*f*(*x*,*y*) instead of*f*((*x*,*y*)).

- In mathematics, a

(That is, the same pair of parentheses is used to indicate both function application and the formation of an ordered pair.)