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 doesn't 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 isn't in general a total function since a Turing machine doesn't 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:
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CHAPTER LXIII
It is now time that I should say something of the infamous bull
Tellier and his friends was forced upon the Pope and the world.
I need not enter into a very lengthy account of the celebrated Papal
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