## Foundations of Mathematics## Set Theory |

## What is a null or empty set? |

A null or empty set contains no elements; an empty set is considered to be a subset of every other set. The opposite of an empty set is, logically, a *nonempty* set, or one that is not empty. The notations for empty set are { } and ∅, but not ( ), as it is sometimes written in texts. Interestingly enough, an empty set is considered to be both open and closed for any set *X*.