and for any partial computable function f there is an e such that, for all x, f(x) = ?(e,x), where the equality means that either both sides are undefined or both are defined and are equal. It is common to write ?_e(x) for ?(e,x); thus the sequence ?₀, ?₁, ... is an enumeration of all partial computable functions. Such enumerations are formally called computable numberings of the partial computable functions.

An arbitrary numbering ? of partial functions