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The omega constant is a mathematical constant defined as the unique real number that satisfies the equation = It is the value of W(1), where W is Lambert's W function. The name is derived from the alternate name for Lambert's W function, the omega function. The numerical value of Ω is given by
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol (e.g., an alphabet letter), or by mathematicians' names to facilitate using it across multiple mathematical problems. [1]
the omega constant 0.5671432904097838729999686622... an asymptotic lower bound notation related to big O notation; in probability theory and statistical mechanics, the support; a solid angle; the omega baryon; the arithmetic function counting a number's prime factors counted with multiplicity; the density parameter in cosmology
In the computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) [1] or halting probability is a real number that, informally speaking, represents the probability that a randomly constructed program will halt.
Olbers' paradox-- Olech theorem-- OLGA (technology)-- Olimpíada Brasileira de Matemática-- Olimpíada Brasileira de Matemática das Escolas Públicas-- Olimpíada de Matemática do Grande ABC-- Oliver Sin-- Olog-- Oloid-- Olympiade Mathématique Belge-- OMDoc-- Omega and agemo subgroup-- Omega-categorical theory-- Omega constant-- Omega equation-- Omega function-- Omega-logic-- Omega ratio ...
Name Standard symbol Definition Field of application Archimedes number: Ar = fluid mechanics (motion of fluids due to density differences) : Asakuma number: As = heat transfer (ratio of heat generation of microwave dielectric heating to thermal diffusion [6]
Any non-computable number, in particular: Chaitin's constant. Constructed irrational numbers which are not simply normal in any base. [30] Any number for which the digits with respect to some fixed base form a Sturmian word. [31] The Prouhet–Thue–Morse constant [32] and the related rabbit constant. [33] The Komornik–Loreti constant. [34]
Let T be PA together with the axioms c ≠ n for each natural number n, where c is a new constant added to the language. Then T is arithmetically sound (as any nonstandard model of PA can be expanded to a model of T ), but ω-inconsistent (as it proves ∃ x c = x {\displaystyle \exists x\,c=x} , and c ≠ n for every number n ).