Numbering (computer science)

A numbering of a set , in the sense of the computability theory , is a possibly partial surjective function . ${\displaystyle M}$ ${\displaystyle \nu :\mathbb {N} \to _{p}M}$

Numbering and the related notations are e.g. B. Tools to prove the equivalence of register and Turing machines .

If the allocation can be calculated , one speaks of an effective numbering .

Remarks

• You forgive all one number with . ${\displaystyle m\in M}$ ${\displaystyle n\in \mathbb {N} }$ ${\displaystyle \nu (n)=m}$
• Not all numbers have to be assigned, e.g. B. . This means: the value at position 3 is undefined or a register machine whose machine function is would get into an endless loop with input 3 . ${\displaystyle \nu (3)=\bot }$ ${\displaystyle \nu }$
• One can also have several numbers. ${\displaystyle m\in M}$