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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
1900 to 1600 BCE [2] Tau: 6.28318 53071 79586 47692 [3] [OEIS 2] Ratio of a circle's circumference to its radius. Equal to : 1900 to 1600 BCE [2] Square root of 2, Pythagoras constant [4] 1.41421 35623 73095 04880 [Mw 2] [OEIS 3] Positive root of =
the time constant of any device, such as an RC circuit; proper time in relativity; one turn: the constant ratio of a circle's circumference to its radius, with value (6.283...). [7] Kendall tau rank correlation coefficient, a measure of rank correlation in statistics; Ramanujan's tau function in number theory
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In mathematical logic, an ω-consistent (or omega-consistent, also called numerically segregative) [1] theory is a theory (collection of sentences) that is not only (syntactically) consistent [2] (that is, does not prove a contradiction), but also avoids proving certain infinite combinations of sentences that are intuitively contradictory.
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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.