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Sequences and Limits
University of Applied Sciences, Augsburg, Germany
- 1 University of Applied Sciences, Augsburg, Germany
Advances in Pure Mathematics·Volume 05 (2015)·Pages 59–61·Published 26 January 2015·DOI10.4236/apm.2015.52007
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Abstract
It is widely held that irrational numbers can be represented by infinite digit-sequences. We will show that this is not possible. A digit sequence is only an abbreviated notation for an infinite sequence of rational partial sums. As limits of sequences, irrational numbers are incommensurable with any grid of decimal fractions.
KeywordsSeriesSequencesLimitsDefinability of Real NumbersSet Theory
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