Empty Set

Topics: Calculus

---

The empty set is the set containing to elements. Its cardinality is $0$.

Open and Closed

Note that $\varnothing$ is open, since $\text{int}(\varnothing )=\varnothing$ (see interior).

$\varnothing$ is also closed, since ${\varnothing }^c=X$ is open (where $X$ is the set we’re working with).