Chaitin's Constant

A Chaitin constant, or Chaitin omega number, also called a halting probability, is a real number that, informally, represents the probability that a randomly constructed computer program will halt, a construction due to Gregory Chaitin in the field of algorithmic information theory. There are infinitely many halting probabilities, one for each method of encoding programs, but it is common to use the Greek letter omega to refer to them as if there were only one, and the construction is sometimes called Chaitin's construction when no specific encoding is meant. Every halting probability is a normal, transcendental real number that is not computable, meaning no algorithm can compute its digits, and it is Martin-Lof random, meaning no algorithm can even reliably guess its digits.