Empty set

The empty set, denoted by $\{\}$ or the Scandinavian symbol $\emptyset$, is the artifically contrived set that does not contain any elements.

Creating such a structure may seem counterintuitive (how can we have a collection of zero elements?), but it is necessary to serve as a placeholder in order to represent certain calculations when dealing with sets. For example, having the empty set allows us to define the intersection of any two sets, even when the sets don't share any elements. In a sense, the empty set is the set theoretical analogue of the number zero.