Encyclopedia > Partial function

  Article Content

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:

All Wikipedia text is available under the terms of the GNU Free Documentation License

  Search Encyclopedia

Search over one million articles, find something about almost anything!
  Featured Article

... 190s 200s 210s 220s 230s - 240s - 250s 260s 270s 280s 290s Years: 237 238 239 240 241 - 242 - 243 244 245 246 247 Events Patriarch Titus[?] succeeds ...

This page was created in 33.2 ms