@TedShifrin Do you know of a single nice $K(G, n)$ with $n>2$? Or $n=2$ and $G \neq \Bbb Z$? Or are the spaces necessarily so silly at that point you just can't describe them in any pleasant geometric way?
Hah. This paper states that for small enough $\epsilon>0$ and very large $n$, $n^2*e^{-\frac{\epsilon^2 (1-\epsilon)}{3}*\frac{7}{\epsilon^2} ln(n)}=o(1)$
I am extremely talented @Will. If we rewrite it as $n^2*e^{\frac{7ln(n)}{\epsilon}*\frac{2\epsilon^2-\epsilon}{2(1-\epsilon)^2}}$ would be o(1) too. Right?
George Orwell, in his famous 1946 essay, “Politics and the English Language,” argued that the battle against poor English wasn’t frivolous because “the slovenliness of our language makes it easier for us to have foolish thoughts.”
@robjohn might have been the image(latex links) that I drag dropped from AoPS
@robjohn might have been the image(latex links) that I drag dropped from AoPS .. but last night I removed all of them .. and wrote them down myself .. is it still not working ? :o
Let $S$ be a nonempty set of positive nonzero integers such that if $x$ is in $S$ then both $4x$ and $\lfloor \sqrt{x} \rfloor$ are in $S$. Prove that $S = \Bbb N \setminus \{0\}$.
The way I solved it used almost no NT though. Mostly analysis.
@Hippalectryon You can't work with absolutely nothing! Prove that $1 \in S$
