Past exam of the year 1 of the computer science course of the University of Oxford / 2003 / Functional programming, data structures and algorithms, procedural programming, and digital hardware / 2 / a / iii / Solution

Idempotence concerns applying an operation to the same whole value. It says more than saying that the equal-entry pairs are unchanged. Choose the idempotent binary operation min. ThenMore generally, a finite list of length $m$ paired with itself produces $m^2$ entries, so length alone contradicts idempotence when $m>1$. Therefore