Dictionary

empty set en · NOUN

Pronunciation

• (Southern-England) audio

Meanings

1. The unique set that contains no elements, denoted ∅ or {}.
   • 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 58:
   • Their existence can be generated on the basis of the empty set, since one is simply the set of the empty set, two is simply that set plus the empty set and so forth. 2008, Sam Gillespie, The Mathematics of Novelty: Badiou's Minimalist Metaphysics, re.press, page 57:
   • 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:
   • 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, by definition of identity of sets. In other words, there's only one empty set. This unique empty set is our building block. Next comes the set whose only member is—the empty set. This set is not empty. 1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257:

Forms

Relateds

singleton set

Synonyms

null set (set containing no elements)

Translations (26)

ro mulțime vidă (unique set that contains no elements) · hu üres halmaz (unique set that contains no elements) · lv tukša kopa (unique set that contains no elements) · vi tập rỗng (unique set that contains no elements) · cs prázdná množina (unique set that contains no elements) · sk prázdna množina (unique set that contains no elements) · ru пусто́е мно́жество (unique set that contains no elements) · pt conjunto vazio (unique set that contains no elements) · gl conxunto baleiro (unique set that contains no elements) · pl zbiór pusty (unique set that contains no elements) · bg празно множество (unique set that contains no elements) · fi tyhjä joukko (unique set that contains no elements) · vi tập hợp rỗng (unique set that contains no elements) · nl lege verzameling (unique set that contains no elements) · cy set wag (unique set that contains no elements) · ja 空集合 (unique set that contains no elements) · tl walang-lamang tangkas (unique set that contains no elements) · de leere Menge (unique set that contains no elements) · da tomme mængde (unique set that contains no elements) · fr ensemble vide (unique set that contains no elements) · sv tomma mängden (unique set that contains no elements) · mk пра́зно мно́жество (unique set that contains no elements) · cmn 空集 (unique set that contains no elements) · es conjunto vacío (unique set that contains no elements) · it insieme vuoto (unique set that contains no elements) · et tühi hulk (unique set that contains no elements)