empty set

Noun

1. The unique set that contains no elements, denoted ∅ or {}.
   • Start with the empty set. We define it as “the set of all objects not equal to themselves,” since there are no such objects. All empty sets have the same members—no members at all! Therefore, as sets they're identical,...
   • The existence of the empty set is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever. - 2004, Michael Potter, Set Theory and its Philosophy, Oxford University Press, page...
   • A topological space may be very sparsely endowed with open sets. As we know, some spaces have only two, the empty set and the full space. - 2007, A. K. Sharma, Measure Theory, Discovery Publishing House, page 1: