1.11 Empty Set

Types: N/A
Examples: N/A
Constructions: 1.12 Classic Subset Results Theorem
Generalizations: N/A

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Empty Set

Let

\emptyset = {x : x \neq x}

This set is called the empty set since it has no elements.

We assume, via an axiom, that $\emptyset$ exists. Since there are no elements in $\emptyset$ , the statement $x \in \emptyset$ is false for all objects $x$ .