Going by your definition, max (x:xs) = max x (max xs) = max x (max (head xs) (tail xs)) = ... ad infinitum. The basic problem with that definition is that it on

Going by your definition, max (x:xs) = max x (max xs) = max x (max (head xs) (tail xs)) = ... ad infinitum. The basic problem with that definition is that it only really defines max for non-empty lists, otherwise the pattern-matching against (x:xs) will throw an exception. In mathematics maximum and minimum of a set are elements of said set. So the empty set has neither a maximum nor a minimum. There is another pair of terms that obeys the rules you want max and min to obey: supremum and infimum: <https://en.wikipedia.org/wiki/Infimum_and_supremum https://en.wikipedia.org/wiki/Infimum_and_supremum>. And indeed supremum of the empty set is -inf. And infimum of the empty set is +inf. That’s because supremum and infimum of a set don’t need to belong to said set. They only need to belong to the set of bounds (upper for supremum; lower for infimum) of said set.