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empty set

File:Nullset.svg · Wikimedia Commons · See Wikimedia Commons

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empty set

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Also known as null set

set (in mathematics) containing no elements

AI overview

An empty set is a collection that contains nothing at all — no items, no members, no elements inside it. It matters in mathematics because it serves as a foundation for building logical systems and helps mathematicians precisely define and reason about collections of things.

AI-generated from the Wikipedia summary — may contain errors.

~14 min read

Encyclopedic overview

The empty set is the set containing no elements. In mathematics, the empty set or void set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set.

Any set other than the empty set is called non-empty.

Excerpted from Wikipedia’s “empty set” article, available under the CC BY-SA 4.0 licence.

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