Finite number of steps 2 (own)
Start with any real number other than $0,\pm 1$. At each step, replace the number $x$ by either $1/x$ or $(x-1)/(x+1)$. Prove that, if we can get from $a$ to $b$ in a finite number of steps, the maximum number of steps required is three.
"Everything should be made as simple as possible, but not simpler." - Albert Einstein