I know that Graham's number is the biggest number ever used in a mathematical demonstration. Does a similarly unimaginably small number, with any worth of note mathematical property, exist?
Please note that I'm talking about the smallest absolute value, so I don't care about negative numbers, only positive real numbers (and I also don't really care about zero).
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Mauro F.
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1The number zero. – Lee Mosher Jun 30 '17 at 14:33
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Or if you are only interested in positive integers, one. – mlk Jun 30 '17 at 14:34
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@LeeMosher Yeah, I guess you're right, but that's not what I really meant – Mauro F. Jun 30 '17 at 14:34
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11 divided by Graham's number. Even better: Graham's number to the power of negative Graham's number. Even better: ... – Bram28 Jun 30 '17 at 14:35
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1See What is the smallest constant that has explicitly appeared in a published paper?. – Dave L. Renfro Jun 30 '17 at 14:48
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1Are you asking for the smallest strictly positive number that has appeared in a reputable publication and has gained inexplicable publicity? – copper.hat Jun 30 '17 at 14:48
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This one comes from physics, but still interesting, planck's constant $= 6.626, 070 \times 10^{-34}$ – Dando18 Jun 30 '17 at 14:48
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3The value of my trading account is another. It is so small it will fit in the margins. – copper.hat Jun 30 '17 at 14:49
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Any infinitesimal element from non-standard analysis ;-) – Reiner Martin Jun 30 '17 at 14:49
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@ReinerMartin the questions restricts to $\mathbb R^+$ – Dando18 Jun 30 '17 at 14:53
1 Answers
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A number approximated as $1.14894×10^{-9}$ figures into the construction of the regular $65537$-gon. It's the distance between the circumcircle and the in-circle, divided by the cirumradius.
Meaning that if you wanted to construct this polygon and allow $1$ mm distance to distinguish between the polygon and it's circumcircle with a good pencil, the polygon would have to extend more than the distance from New York to Chicago!
Oscar Lanzi
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