$\begingroup$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).
$\endgroup$101 Answer
$\begingroup$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!
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