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 $$S \ne \varnothing$$.