Re:The Mystery of 355/113
by michaelf on Tuesday July 24, 2012 @11:36PM
(#4289239)
Is it also the case that all transcendental numbers have approximations of unbounded quality? Or only that Liouville numbers have approximations of unbounded quality, and therefore cannot be algebraic?
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Liouville numbers have approximations of unbounded quality and thus cannot be algebraic. "Most" transcendental numbers only have finitely many approximations of quality higher than 2 + epsilon for any epsilon.