0.999… = 1: An Infinitesimal Explanation

Dawson, C. Bryan

doi:10.4169/mathhorizons.24.2.5

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2017

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“…. where the limit of a sequence (u n ) is defined, following any calculus textbook, as the real number L such that for every ǫ > 0 there exists an N > 0 such that if n > N then |u n − L| < ǫ (and even in the hyperreal number system they are still equal, as Bryan Dawson recently noted in [Dawson 2016]).…”

Section: Introductionmentioning

confidence: 99%

Analyzing Benardete's comment on decimal notation

Bair,

Blaszczyk,

Katz

et al. 2017

Preprint

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Philosopher Benardete challenged both the conventional wisdom and the received mathematical treatment of zero, dot, nine recurring. An initially puzzling passage in Benardete on the intelligibility of the continuum reveals challenging insights into number systems, the foundations of modern analysis, and mathematics education. A key concept here is, in Terry Tao's terminology, that of an ultralimit.

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Section: Introductionmentioning

confidence: 99%