PARTIAL FUNCTION

Domain	Definition
Computing	Partial function A function which is not defined for all arguments of its input type. E.g. f(x) = 1/x if x /= 0. The opposite of a total function. In denotational semantics, a partial function f : D -> C may be represented as a total function ft : D' -> lift(C) where D' is a superset of D and ft x = f x if x in D ft x = bottom otherwise where lift(C) = C U bottom. Bottom (LaTeX \perp) denotes "undefined". (1995-02-03). Source: The Free On-line Dictionary of Computing.
Math	A function which is not defined for some of its domain. For instance, division is (usually) a partial function since anything divided by 0 is undefined. (references)
Source: compiled by the editor from various references; see credits.

Specialty Definition: Partial function

In mathematics and computer science, a partial function, from the domain X to the codomain Y is a binary relation, over X and Y, which is functional, that is, associates with every element in set X with, at most, one element in set Y. If a partial function associates with every element in its domain precisely one element of its codomain, then it is a "total function". Note that with this terminology, not every partial function is a "true" function.

This above diagron does not represent a "well-defined" function; because, the element 1, in X, is associated with nothing.

The Turing Machine

Partial functions are often used in theoretical computer science: the behavior of a Turing machine for instance can be described by a partial function relating its inputs to its outputs. This is not in general a total function since a Turing machine does not always produce an output for every input: it can run into an infinite loop. Even worse, it can run into an infinite loop for different inputs.

See also:

multivalued function

Anagrams: PARTIAL FUNCTION

Scrabble® Enable2K-Verified Anagrams
	Words within the letters "a-a-c-f-i-i-l-n-n-o-p-r-t-t-u"
	-3 letters: articulation, capitulation, contrapuntal.
	-4 letters: anticipator, facilitator, inculpation, infatuation, nutritional, puritanical, unpatriotic.
	-5 letters: anticipant, capitation, citational, connatural, culinarian, filtration, flirtation, fractional, frictional, functional, infarction, infraction, noncapital, nonfactual, nutational, patination, plantation, pontifical, punctation, tinctorial, tractional, truncation, urtication.
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