The Irrationality Exponents of Computable Numbers
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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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
03.10.2014
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Subjects | |
Online Access | Get full text |
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Summary: | 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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DOI: | 10.48550/arxiv.1410.1017 |