empty set
empty set noun: the unique set that contains no elements, denoted ∅ or {}.
Noun
empty set (plural empty sets)
- 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, by definition of identity of sets. In other words, there's only one empty set....1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257
- 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
- Synonyms:
- null set
empty set meaning in Tamil, Tagalog and Vietnamese
empty set in Tamil
- வெற்று கணம்
empty set in Tagalog
- unique set that contains no elements
- walang-lamang tangkas
empty set in Vietnamese
- unique set that contains no elements
- tập hợp rỗng, tập rỗng
Examples of empty set in a sentence
- All empty sets have the same members—no members at all!1997, Reuben Hersh, What Is Mathematics, Really?, Oxford University Press, page 257:
- 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:
- 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:
Synonyms of empty set
Forms of empty set
| plural | empty sets |
|---|
Questions about empty set
- What does empty set mean?
- Empty set means the unique set that contains no elements, denoted ∅ or {}.
- What is empty set in Tamil?
- Empty set in Tamil is வெற்று கணம். See Empty set meaning in Tamil.
- How do you use empty set in a sentence?
- All empty sets have the same members—no members at all!
- What part of speech is empty set?
- Empty set is a noun.
- What is the plural of empty set?
- The plural of empty set is empty sets.
Words near empty set in the dictionary
Source and license
Adapted from Wiktionary: empty set (page history and authors); empty set (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Pronunciation audio from Wikimedia Commons, each file under its own free license: LL-Q1860 (eng)-Vealhurl-empty set.wav.
Cite this entry: “empty set.” Word.ws, https://word.ws/empty_set. Based on Wiktionary, CC BY-SA 4.0.