total function

In mathematics, a partial function is a binary relation that associates each element of a set, sometimes called its domain, with at most one element of another (possibly the same) set, called its codomain. However, not every element of the domain has to be associated with an element of the codomain.An example of a partial function with domain and codomain equal to the integers, is given by where g(n) is only defined for those nonnegative integers which are perfect squares, that is are equal to the square of some integer.
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<mathematics> A function which is defined for all arguments of the appropriate type. The opposite is a partial function.
(1997-01-10)