# Difference between revisions of "Set System"

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== References == | == References == | ||

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− | * (Wikipedia, | + | * (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Algebra_of_sets Retrieved:2019-11-10. |

− | + | ** The '''algebra of sets''' defines the properties and laws of [[Set (mathematics)|sets]], the set-theoretic [[operation (mathematics)|operations]] of [[union (set theory)|union]], [[intersection (set theory)|intersection]], and [[complement (set theory)|complementation]] and the [[binary relation|relations]] of set [[equality (mathematics)|equality]] and set [[subset|inclusion]]. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. <P> Any set of sets closed under the set-theoretic operations forms a [[Boolean algebra (structure)|Boolean algebra]] with the join operator being ''union'', the meet operator being ''intersection'', the complement operator being ''set complement'', the bottom being <math> \varnothing </math> and the top being the [[universe (mathematics)|universe set under consideration]]. | |

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=== 1966 === | === 1966 === | ||

* Paul J Cohen. (1966). “[http://www.amazon.com/Theory-Continuum-Hypothesis-Dover-Mathematics/dp/0486469212/ Set Theory and the Continuum Hypothesis]." W. A. Benjamin, Inc. | * Paul J Cohen. (1966). “[http://www.amazon.com/Theory-Continuum-Hypothesis-Dover-Mathematics/dp/0486469212/ Set Theory and the Continuum Hypothesis]." W. A. Benjamin, Inc. | ||

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__NOTOC__ | __NOTOC__ | ||

[[Category:Concept]] | [[Category:Concept]] | ||

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## Revision as of 22:59, 10 November 2019

A Set System is a Formal System for sets and Set Operations.

**AKA:**Set Theory, Set Formal System, Formal Set System, Set Algebra, Algebra of Sets, [math](V,\mathcal{I})[/math].**Context:**- It must include Set Operations (that can be constrained by Set Axioms).
- It must include a Set Formal Language.
- It can range from being an Independent Set System to being a Dependent System System.

**Counter-Example(s):****See:**Multiset, Rough Set Theory, Infinite Set, Empty Set, Countable Set, Matroid, Discrete Mathematics.

## References

### 2019

- (Wikipedia, 2019) ⇒ https://en.wikipedia.org/wiki/Algebra_of_sets Retrieved:2019-11-10.
- The
**algebra of sets**defines the properties and laws of sets, the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.Any set of sets closed under the set-theoretic operations forms a Boolean algebra with the join operator being

*union*, the meet operator being*intersection*, the complement operator being*set complement*, the bottom being [math] \varnothing [/math] and the top being the universe set under consideration.

- The

### 1966

- Paul J Cohen. (1966). “Set Theory and the Continuum Hypothesis." W. A. Benjamin, Inc.