Mike Spivey
Reputation
238/100 score
 2d awarded Necromancer Mar19 awarded Favorite Question Mar10 awarded Announcer Jan29 awarded Famous Question Jan15 awarded Popular Question Jan14 awarded Nice Answer Jan5 awarded Nice Answer Jan5 comment Proving that $f(n)=n$ if $f(n+1)>f(f(n))$ @SouvikDey: Since $f$ maps $f(k-1)$ to some value strictly smaller than $n$, the induction hypothesis applies, and so $f(f(k-1)) = f(k-1)$. (The induction hypothesis is stated in the first paragraph of Claim 3; namely, that if $f$ maps $k$ to some value $0 \leq m < n$, then the input $k$ is equal to the output $m$. The claim $f(f(k-1)) = f(k-1)$ is just saying that the input $f(k-1)$ is equal to the output $f(f(k-1))$.) Jan4 awarded Good Answer Dec31 awarded Great Answer Dec18 awarded Notable Question Dec9 awarded Caucus Nov26 awarded Nice Answer Nov17 awarded Enlightened Nov17 awarded Nice Answer Nov17 awarded Good Question Oct26 awarded Nice Answer Oct16 revised How to convert a fraction into ternary? fixed math typo Oct16 comment How to convert a fraction into ternary? @zzzzBov: Good catch! I'll fix it. Oct15 awarded Good Answer