# Difference between revisions of "Universal Set"

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− | A [[Universal Set]] is a [[set]] that contains all [[ | + | A [[Universal Set]] is a [[set]] that contains all [[object]]s, including itself. |

* <B>AKA:</B> [[Set Universe]]. | * <B>AKA:</B> [[Set Universe]]. | ||

− | * <B>See:</B> [[Complement Set Operation]], | + | * <B> Context: </B> |

+ | * It is usually denoted by the capital letter, <math>U</math>. | ||

+ | * <B>Example(s):</B> | ||

+ | ** The [[complement]] of an [[empty set]]. | ||

+ | * <B>Counter-Example(s):</B> | ||

+ | ** an [[Empty Set]], | ||

+ | ** a [[Subset]]. | ||

+ | * <B>See:</B> [[Complement Set Operation]], [[Grothendieck Universe]], [[Domain of Discourse]]. | ||

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## Revision as of 23:38, 10 November 2019

A Universal Set is a set that contains all objects, including itself.

**AKA:**Set Universe.**Context:**- It is usually denoted by the capital letter, [math]U[/math].
**Example(s):**- The complement of an empty set.

**Counter-Example(s):****See:**Complement Set Operation, Grothendieck Universe, Domain of Discourse.

## References

### 2019a

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Universal_set Retrieved:2019-11-10.
- In set theory, a
**universal set**is a set which contains all objects, including itself.^{[1]}In set theory as usually formulated, the conception of a universal set leads to Russell's paradox and is consequently not allowed. However, some non-standard variants of set theory include a universal set.

- In set theory, a

### 2019b

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Universe_(mathematics) Retrieved:2019-11-10.
- In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a
**universe**is a collection that contains all the entities one wishes to consider in a given situation. It is related to the concept of a domain of discourse in philosophy.In set theory, universes are often classes that contain (as elements) all sets for which one hopes to prove a particular theorem. These classes can serve as inner models for various axiomatic systems such as ZFC or Morse–Kelley set theory. Universes are of critical importance to formalizing concepts in category theory inside set-theoretical foundations. For instance, the canonical motivating example of a category is

**Set**, the category of all sets, which cannot be formalized in a set theory without some notion of a universe.In type theory, a universe is a type whose elements are types.

- In mathematics, and particularly in set theory, category theory, type theory, and the foundations of mathematics, a

- ↑ Forster 1995 p. 1.