Definition:Unit of System of Sets

Let $$\mathcal{S}$$ be a system of sets.

Let $$U \in \mathcal{S}$$ such that:
 * $$\forall A \in \mathcal{S}: A \cap U = A$$

Then $$U$$ is the unit of $$\mathcal{S}$$.

Note that, for a given system of sets, if $$U$$ exists then it is unique.