| Information | |
|---|---|
| has gloss | (noun) (mathematics) the set that contains all the elements or objects involved in the problem under consideration; "all other sets are subsets of the universal set" universal set |
| has gloss | eng: In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, the conception of a set of all sets leads to a paradox. The reason for this lies with the parameters of Zermelos axiom of separation: for any formula \varphi(x) and set A, the set \x \in A \mid \varphi(x)\} which contains exactly those elements x of A that satisfy \varphi exists. If the universal set V existed, then Russells paradox could be resolved by considering \x \in V\mid x\not\in x\}. More generally, for any set A we can prove that \x \in A\mid x\not\in x\} is not an element of A. |
| lexicalization | eng: Set of all sets |
| lexicalization | eng: universal set |
| subclass of | (noun) (mathematics) an abstract collection of numbers or symbols; "the set of prime numbers is infinite" set |
| Meaning | |
|---|---|
| Belarusian | |
| has gloss | bel: Унівэрса́льнае мно́ства (унівэрсуюм) — мноства, якое ўлучае ў сябе ўсе магчымыя элемэнты. Калі некаторы аб’ект зьяўляецца элемэнтам якога-небудзь мноства, то ён адначасова зьяўляецца і элемэнтам унівэрсальнага мноства. |
| lexicalization | bel: універсальнае мноства |
| lexicalization | bel: Унівэрсальнае мноства |
| Bengali | |
| lexicalization | ben: সার্বিক সেট |
| Croatian | |
| lexicalization | hrv: univerzalni skup |
| Icelandic | |
| has gloss | isl: Almengi er hugtak í heimspeki og mengjafræði, sem á við hugsanlegt mengi, sem inniheldur öll önnur mengi, þ.e. megi allra mengja. Slíkt mengi innihéldi þá einnig sjálft sig, en fyrifinnst ekki skv. Zermelo Fraenkel mengjafræði. Ef gert er ráð fyrir mengi allra mengja, sem ekki innihalda sjálft sig fæst Russell mótsögnin. |
| lexicalization | isl: Almengi |
| Italian | |
| has gloss | ita: Nella teoria degli insiemi si indica con insieme universo quel particolare insieme che contiene tutti gli elementi e tutti gli insiemi esistenti, compreso quindi anche se stesso e l'insieme vuoto. |
| lexicalization | ita: insieme universo |
| Korean | |
| has gloss | kor: 전체집합(Universal set)은 고려되는 모든 대상을 포함하는 집합을 말한다. 구체적으로는 두 의미로 나뉘는데, 양쪽 모두 전체모임의 개념과 밀접한 연관이 있다. |
| lexicalization | kor: 전체 집합 |
| lexicalization | kor: 전체집합 |
| Maori | |
| Show unreliable ▼ | |
| lexicalization | mri: huinga matua |
| lexicalization | mri: röpü matua |
| Russian | |
| has gloss | rus: Универса́льное мно́жество — в математике множество, содержащее все мыслимые объекты. Универсальное множество единственно. |
| lexicalization | rus: универсальное множество |
| Kalmyk | |
| has gloss | xal: Олна онлд, нег чигн олн һарһл уга олн Бүгдə олн болхв. |
| lexicalization | xal: Бүгдə олн |
| Links | |
|---|---|
| has category | (noun) a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement maths, math, mathematics |
| similar | e/Universal set |
| Media | |
|---|---|
| media:img | Absolute complement.svg |
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