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## Susan D'Agostino

Print publication date: 2020

Print ISBN-13: 9780198843597

Published to Oxford Scholarship Online: April 2020

DOI: 10.1093/oso/9780198843597.001.0001

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# Keep it simple whenever possible, since 0.999…=1

Chapter:
(p.151) 25 Keep it simple whenever possible, since $0.999…=1$
Source:
How to Free Your Inner Mathematician
Publisher:
Oxford University Press
DOI:10.1093/oso/9780198843597.003.0026

“Keep it simple whenever possible, since 0.999…=1” presents and discusses a very short mathematical proof demonstrating the long-known result that 0.999…=1. The ellipsis in the number 0.999… indicates that this number repeats in an infinite decimal expansion. As such, this number is unwieldy to lug around, insert into equations, and even describe. However, the number 1 is not simply a good approximation for 0.999…., but rather the number 1 may be used in place of 0.999… without loss of information. Mathematics students and enthusiasts are encouraged to keep their mathematical and life pursuits simple whenever possible. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Keywords:   proof, 0.999…=1, math, student, number 1

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