Sequences and Limits - Advances in Pure Mathematics

APM > Vol.5 No.2, February 2015

Advances in Pure Mathematics

Volume 5, Issue 2 (February 2015)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

Google-based Impact Factor: 0.50 Citations h5-index & Ranking

Sequences and Limits ()

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DOI: 10.4236/apm.2015.52007 4,219 Downloads 6,212 Views Citations

Author(s)

Wolfgang Mueckenheim^*

Affiliation(s)

University of Applied Sciences, Augsburg, Germany.

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.

KEYWORDS

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

Share and Cite:

Mueckenheim, W. (2015) Sequences and Limits. Advances in Pure Mathematics, 5, 59-61. doi: 10.4236/apm.2015.52007.

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