set theory


set theory

Operations on Sets Set Theory - Axiomatic Set Theoryset theoryNOUNset theory (noun) the branch of mathematics which deals with the formal properties of sets as units (without regard to the nature of their individual constituents) and the expression of other branches of mathematics in terms of sets.Set Theory (Stanford Encyclopedia of Philosophy)

Set theory,as a separate mathematical discipline,begins in thework of Georg Cantor.One might say that set theory was born in late1873,when he made the amazing discovery that the linear continuum,that is,the real line,is not countable,meaning that its pointscannot be counted using the natural numbers.So,even though the setof natural numbers and the set of real numbers are both infinite,there are more real nuThe Axioms of Set TheoryThe Theory of Transfinite Ordinals and CardinalsThe Universe Vv of All SetsSet Theory as The Foundation of MathematicsThe Set Theory of The ContinuumGödels Constructible UniverseForcingThe Search For New AxiomsLarge CardinalsZFC is an axiom system formulated in first-order logic withequality and with only one binary relation symbol formembership.Thus,we write AB to express that A is a member ofthe set B.See the Supplement on Basic Set Theory for further details.See also the Supplement on Zermelo-Fraenkel Set Theory for a formalized version of the axioms and further comments.Westate below the axioms of ZFC informally.See more on plato.stanford.eduExplore furtherset theory Symbols,Examples, Formulas BritannicabritannicaSet Theory Introduction to College Mathematicscourses.lumenlearningAN INTRODUCTION TO SET THEORY - University of Toronto Set Theory,Part 1 lesson plan Spiralspiral.acSets Activities for High School Math StudystudyRecommended to you based on what's popular Feedbackset theory Symbols,Examples, Formulas BritannicaSet theory,branch of mathematics that deals with the properties of well-defined collections of objects,which may or may not be of a mathematical nature,such as numbers or functions.The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts.


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