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Sequences and Limits

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DOI: 10.4236/apm.2015.52007    3,384 Downloads   4,518 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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

References

[1] Mueckenheim, W. (2011) Mathematik für die ersten Semester. 3rd Edition, Oldenbourg Verlag GmbH, Muenchen, 193.
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[2] Cantor, G. (1889) Bemerkungen mit Bezug auf den Aufsatz: Zur Weierstra?-Cantorschen Theorie der Irrationalzahlen. Mathematische Annalen, 33, 476. http://dx.doi.org/10.1007/BF01443973
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http://static.sdu.dk/mediafiles//Files/Om_SDU/Centre/C_NAMADI/Skriftserie/MACAS_samlet.pdf%

  
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