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arXiv · 1410.1017

The Irrationality Exponents of Computable Numbers

Verónica Becher·Yann Bugeaud·Theodore A. Slaman
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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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Verónica Becher, Yann Bugeaud, Theodore A. Slaman. 2014-10-04. The Irrationality Exponents of Computable Numbers. https://arxiv.org/abs/1410.1017

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