The number of distinct nonisomorphic semigroups with one element is one.
[2][3] In spite of its extreme triviality, the semigroup with one element is important in many situations.
It is the starting point for understanding the structure of semigroups.
It serves as a counterexample in illuminating many situations.
In the language of category theory, any semigroup with one element is a terminal object in the category of semigroups.