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).