Empty set - Knowlpedia

The empty set, denoted $\varnothing$ , is the set with no elements:

\forall x\,(x\notin \varnothing).

Remarks

By extensionality (see set), there is only one such set: if $E$ and $F$ have no elements, then $E=F$ . The empty set is the identity for union and an absorbing element for intersection when working with subsets of a fixed ambient set.

Examples

The solution set $\{x\in\mathbb{R} : x^2+1=0\}$ is $\varnothing$ .
If $A$ and $B$ are disjoint subsets of a set, then $A\cap B=\varnothing$ .