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.

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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 N⁺ to Q.

    Set-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)).

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

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