Cardinality of Empty Set

Theorem

 * $\left|{S}\right| = 0 \iff S = \varnothing$

That is, the empty set is finite, and has a cardinality of zero.

Proof
From the definition of $\varnothing$, $\varnothing$ is the set with no elements.

The result follows from this and the definition of cardinality.

Alternative Treatment
Some sources define zero as the cardinality of the empty set.