Question 141
Let $S = \mathbb{N} \cup \{1/n \mid n \in \mathbb{N}\}$ be the set of all positive integers and their reciprocals. A function $f : S \to S$, defined on $S$ and with values in $S$, is called *semi-reciprocal* if $f(f(x)) = 1/x$ for all $x \in S$.
a. Find a semi-reciprocal function.
b. Show that for every semi-reciprocal function $f$ there is exactly one number $p \in S$ such that $f(p) = p$.
a. Find a semi-reciprocal function.
b. Show that for every semi-reciprocal function $f$ there is exactly one number $p \in S$ such that $f(p) = p$.