Editing Chaitin's constant (section)

== Definition ==
Let {{math|''P''{{sub|F}}}} be the domain of a prefix-free universal computable function {{mvar|F}}.  The constant {{math|&Omega;{{sub|''F''}}}} is then defined as

<math display="block">\Omega_F = \sum_{p \in P_F} 2^{-|p|},</math>

where {{math|{{abs|''p''}}}} denotes the length of a string {{mvar|p}}. This is an [[series (mathematics)|infinite sum]] which has one summand for every {{mvar|p}} in the domain of {{mvar|F}}. The requirement that the domain be prefix-free, together with [[Kraft's inequality]], ensures that this sum converges to a [[real number]] between 0 and 1. If {{mvar|F}} is clear from context then {{math|&Omega;{{sub|''F''}}}} may be denoted simply {{math|&Omega;}}, although different prefix-free universal computable functions lead to different values of {{math|&Omega;}}.