empty set

Noun

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Noun

**empty set** (*plural* empty sets)

- (
*set theory*) The unique set that contains no elements, denoted ∅*or*{}.**1997**, Reuben Hersh,*What Is Mathematics, Really?*, Oxford University Press, page 257 ↗,- 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.

- Start with the
**2004**, Michael Potter,*Set Theory and its Philosophy*, Oxford University Press, page 58 ↗,- The existence of the
**empty set**is entailed, in the presence of the axiom scheme of separation, by the existence of any set whatever.

- The existence of the
**2007**, A. K. Sharma,*Measure Theory*, Discovery Publishing House, page 1 ↗,- 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.

- A topological space may be very sparsely endowed with open sets. As we know, some spaces have only two, the
**2008**, Sam Gillespie,*The Mathematics of Novelty: Badiou's Minimalist Metaphysics*, re.press, page 57 ↗,- 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.

- Their existence can be generated on the basis of the

- (
*set containing no elements*) null set

- French: ensemble vide
- German: leere Menge
- Italian: insieme vuoto
- Portuguese: conjunto vazio
- Russian: пусто́е мно́жество
- Spanish: conjunto vacío

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004