Complete Numbering - Definition

Definition

A numbering of a set is called complete (with respect to an element ) if for every partial computable function there exists a total computable function so that

 \nu \circ h(i) =
\left\{
\begin{matrix}
\nu \circ f(i) &\mbox{if}\ i \in \mathrm{dom}(f), \\
a &\mbox{otherwise}.
\end{matrix}
\right.

The numbering is called precomplete if

Read more about this topic:  Complete Numbering

Famous quotes containing the word definition:

    The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.
    Samuel Taylor Coleridge (1772–1834)

    The man who knows governments most completely is he who troubles himself least about a definition which shall give their essence. Enjoying an intimate acquaintance with all their particularities in turn, he would naturally regard an abstract conception in which these were unified as a thing more misleading than enlightening.
    William James (1842–1910)

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)