Definitions for universal set
uni·ver·sal set

Princeton's WordNetRate this definition:0.0 / 0 votes

1. universal setnoun

   (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"

WiktionaryRate this definition:0.0 / 0 votes

1. universal setnoun

   A set large enough to contain all sets under consideration in the current context.

WikipediaRate this definition:0.0 / 0 votes

1. Universal set

   In set theory, a universal set is a set which contains all objects, including itself. In set theory as usually formulated, it can be proven in multiple ways that a universal set does not exist. However, some non-standard variants of set theory include a universal set.

ChatGPTRate this definition:0.0 / 0 votes

1. universal set

   A universal set is the set that contains all objects or elements under consideration for a particular discussion or problem. It is usually denoted by the symbol U. In other words, any set or element that is relevant to a particular analysis is part of the universal set.

WikidataRate this definition:0.0 / 0 votes

1. Universal set

   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 Zermelo's axiom of comprehension: for any formula and set A, there exists a set which contains exactly those elements x of A that satisfy . If the universal set V existed and the axiom of separation applied to it, then Russell's paradox would arise from Generally, for any set A we can prove that is not an element of A. A second difficulty is that the power set of the set of all sets would be a subset of the set of all sets, provided that both exist. This conflicts with Cantor's theorem that the power set of any set always has strictly higher cardinality than the set itself. The idea of a universal set seems intuitively desirable in the Zermelo–Fraenkel set theory, particularly because most versions of this theory do allow the use of quantifiers over all sets. This is handled by allowing carefully circumscribed mention of V and similar large collections as proper classes. In theories in which the universe is a proper class, is not true because proper classes cannot be elements.

Suggested ResourcesRate this definition:0.0 / 0 votes

1. universal set

   The universal set symbol -- In this Symbols.com article you will learn about the meaning of the universal set symbol and its characteristic.

Matched Categories

1. • Math
   • Set

How to pronounce universal set?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say universal set in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of universal set in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of universal set in Pythagorean Numerology is: 3

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=universal set
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Universal_Set
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Universal_Set
4. ^ ChatGPT
   https://chat.openai.com
5. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=universal set