Definition:Magma

Definition
A groupoid (or gruppoid) is an algebraic structure $\left({S, \circ}\right)$ which is closed.

Note that as usually defined, $\varnothing \subseteq S$, that is, the underlying set is allowed (in the extreme case) to be the empty set.

However, some treatments insist that $S \ne \varnothing$.

Linguistic note
The word groupoid arises as a back-formation from group in the same way as humanoid derives from human.

The word gruppoid (rarely found in English) is the German term (from the German gruppe for group).