Editing Chaitin's constant (section)

== Incompleteness theorem for halting probabilities ==
{{Main|Chaitin's incompleteness theorem}}

For each specific consistent effectively represented [[axiomatic system]] for the [[natural numbers]], such as [[Peano axioms|Peano arithmetic]], there exists a constant {{mvar|N}} such that no bit of {{math|&Omega;}} after the {{mvar|N}}th can be proven to be 1 or 0 within that system. The constant {{mvar|N}} depends on how the [[formal system]] is effectively represented, and thus does not directly reflect the complexity of the axiomatic system. This incompleteness result is similar to [[Gödel's incompleteness theorem]] in that it shows that no consistent formal theory for arithmetic can be complete.