For example , the semigroup with one element is the only semigroup in which 0 = 1 , that is , the zero element and the identity element are equal .
It serves as a counterexample in illuminating many situations .
The semigroup with one element is the only semigroup in which 0 = 1 , that is , the zero element and the identity element are equal .
It serves as a counterexample in illuminating many situations .