The [[Set]] with no elements ([[Cardinality]] of 0). Denoted by $\emptyset$ or $\set{}$. For any [[Set]] $S$, the [[Empty Set]] is a [[Subset]] of $S$. $\huge \forall S \pa{ \emptyset \in S} $ >[!tldr] Proof Suppose $\emptyset \not\subset S$ Then $\exists x \in \emptyset$ such that $x \not\in S$, but this cannot happen because $|\emptyset|=0$.