Empty set

The empty set.

Inmathematics,theempty setis thesetthat has nothing in it. It is often written as$\varnothing$,$\emptyset$,$\{\}$.For example, consider the set ofintegernumbers between two and three. Since there is nointegerbetween two and three, the set ofintegernumbers between them isempty.

Anystatementabout all elements of the empty set is automaticallytrue.For example, all integers between two and three are greater than seven. This only makes sense because there are no integers between two and three. This kind of truth is calledvacuous truth.

Note that the symbol$\varnothing$comes from the Latin letterØ,and not the Greek letterφ.The empty set is also sometimes called the null set.

Related pages

• Zero