The Irrationality Exponents of Computable Numbers

Published 4 Oct 2014 in math.NT | (1410.1017v1)

Abstract: We prove that a real number a greater than or equal to 2 is the irrationality exponent of some computable real number if and only if a is the upper limit of a computable sequence of rational numbers. Thus, there are computable real numbers whose irrationality exponent is not computable.

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