Numbering (computability theory)

A numbering an amount within the meaning of computability theory, is a potentially partial surjective function.

Numbering and related notations are eg tools in the proof of the equivalence of Registrar and Turing machines.

If the mapping is computable we also speak of an effective numbering.


  • You forgive with a number for all.
  • It need not be awarded every number, for example. This means that the value of the digit 3 is undefined or a register machine, the machine function is, would fall into an infinite loop when you enter 3.
  • One may also have multiple numbers.
  • Computability theory