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Irrationality of limits of quickly convergent algebraic numbers sequences

Author: A. V. Nabutovsky
Journal: Proc. Amer. Math. Soc. 102 (1988), 473-479
MSC: Primary 11J72; Secondary 40A05
MathSciNet review: 928963
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Abstract: We present criteria for irrationality of limits of convergent sequences of rational numbers, algebraic numbers of the same degree and of strictly increasing degrees.

The criterion for irrationality of limits of a sequence of rational numbers has the form of an infinite system of inequalities on successive differences between elements. These inequalities are not strict. If these inequalities are satisfied, then the limit is rational if and only if all inequalities but a finite set of them are satisfied as equalities and the sequence becomes monotonous beginning from some element. So, the criterion permits to see a "border" between rationality and irrationality for some class of quickly convergent sequences.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1988 American Mathematical Society

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