Empty set

In mathematics, the empty set is the set that has nothing in it. It is often written as $\varnothing$, $\emptyset$, $\{\}$. For example, consider the set of integer numbers between two and three. Since there is no integer between two and three, the set of integer numbers between them is empty.

The empty set.

Any statement about all elements of the empty set is automatically true. 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 called vacuous truth.

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

Related pages

• Zero