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Sequences and Limits

DOI: 10.4236/apm.2015.52007, PP. 59-61

Keywords: Series, Sequences, Limits, Definability of Real Numbers, Set Theory

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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.


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