>>225811
Consider the function $f$ defined in the image.
Let $f^{0}(n) = n$ and let $f^{i}(n) = f(f^{i-1}(n))$ for $i > 0$. (That is, $f^{i}(n)$ is the result of applying $f$ iteratively $i$ times to $n$.)

For every $n$, does there exist an $i$ such that $f^{i}(n) = 1$?