Why Does 0.999… Equal 1?
In short: In the real numbers 0.999… equals 1. This film traces decimals and endless processes, gives two accessible arguments, explains why the result feels wrong to so many students, and visits the hyperreal numbers, where the equality can be rejected.
A 1:33 short film in the series “From Fingers to Qubits”, narrated by intellect_voice_01.
Sources used in this film: Encyclopaedia Britannica, “Decimal fraction | mathematics | Britannica”; Academia.edu, hosting Anderson Norton's article "Does 0.999… Really Equal 1?" from The Mathematics Educator (doi:10.63301/TME.V21I2.1969), “Does 0.999… Really Equal 1?”; The Mathematics Educator (University of Georgia), article by Anderson Norton (2012), hosted on Academia.edu, “Does 0.999... Really Equal 1”; Wolfram MathWorld (Eric W. Weisstein, with contributions by Matt Insall), “Nonstandard Analysis -- from Wolfram MathWorld”; Encyclopaedia Britannica, “Pi | Definition, Symbol, Number, History, Applications, & Facts | Britannica”.
Sources used in this film
- Encyclopaedia Britannica — Decimal fraction | mathematics | Britannica · View →
- Academia.edu, hosting Anderson Norton's article "Does 0.999… Really Equal 1?" from The Mathematics Educator (doi:10.63301/TME.V21I2.1969) — Does 0.999… Really Equal 1? · View →
- The Mathematics Educator (University of Georgia), article by Anderson Norton (2012), hosted on Academia.edu — Does 0.999... Really Equal 1 · View →
- Wolfram MathWorld (Eric W. Weisstein, with contributions by Matt Insall) — Nonstandard Analysis -- from Wolfram MathWorld · View →
- Encyclopaedia Britannica — Pi | Definition, Symbol, Number, History, Applications, & Facts | Britannica · View →
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Sources
- Summary by Intellect · source: Encyclopaedia Britannica: Decimal fraction | mathematics | Britannica
- Also: Academia.edu, hosting Anderson Norton's article "Does 0.999… Really Equal 1?" from The Mathematics Educator (doi:10.6330: Does 0.999… Really Equal 1?
- Also: The Mathematics Educator (University of Georgia), article by Anderson Norton (2012), hosted on Academia.edu: Does 0.999... Really Equal 1
- Also: Wolfram MathWorld (Eric W. Weisstein, with contributions by Matt Insall): Nonstandard Analysis -- from Wolfram MathWorld
- Also: Encyclopaedia Britannica: Pi | Definition, Symbol, Number, History, Applications, & Facts | Britannica
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