Empty Set

symbol: $\varnothing$, $\{\}$, or $\varnothing$

The empty set is the unique set with no elements.

• Notation: $\varnothing$ or simply $\{\}$.
• Cardinality: $|\varnothing |=0$.
• The empty set is a subset of every set: $\varnothing \subseteq A$ for all $A$.
• It is the foundation of set theory, all sets can be built starting from $\varnothing$.