Set System
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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]\displaystyle{ (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]\displaystyle{ \varnothing }[/math] and the top being the universe set under consideration.
- 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.
1966
- Paul J Cohen. (1966). “Set Theory and the Continuum Hypothesis." W. A. Benjamin, Inc.