Claim: The trivial group, which should not be confused with the empty set (which has no elements, and lacking an identity element, cannot be a group), is the same as the similarly defined trivial monoid.
Evidence: The trivial group should not be confused with the empty set (which has no elements, and lacking an identity element, cannot be a group). The similarly defined trivial monoid is also a group since its only element is its own inverse, and is hence the same as the trivial group.