Empty set

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the empty set or void set is the unique <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> having no <a href="/facts/Element_(mathematics)/Q2mx1vHL">elements</a>; its size or <a href="/facts/Cardinality/m6VPojwT">cardinality</a> (count of elements in a set) is <a href="/facts/0/4NBRtKHc">zero</a>. Some <a href="/facts/Axiomatic_set_theories/1ptfsvUP">axiomatic set theories</a> ensure that the empty set exists by including an <a href="/facts/Axiom_of_empty_set/eNQLyP1k">axiom of empty set</a>, while in other theories, its existence can be deduced. Many possible properties of sets are <a href="/facts/Vacuously_true/QBsue3pP">vacuously true</a> for the empty set.
Any set other than the empty set is called non-empty.
In some textbooks and popularizations, the empty set is referred to as the "null set". However, <a href="/facts/Null_set/kMudL8Mn">null set</a> is a distinct notion within the context of <a href="/facts/Measure_theory/yCq7zlI4">measure theory</a>, in which it describes a set of measure zero (which is not necessarily empty).

Empty set open-in-new

Empty set