Omega (Chaitin's constant)

Omega (Ω), or Chaitin's constant, is a number that represents the probability that a randomly chosen computer program will halt (stop executing) when run on a universal computer. It is a real number between 0 and 1, encapsulating the inherent unpredictability of whether certain programs will finish or run forever. Omega is uncomputable, meaning no algorithm can determine its exact value, reflecting deep limits in formal mathematics and computation. It embodies the concept of fundamental randomness and complexity within algorithmic information theory.