Set Theory Set theory is a mathematical theory of collections,...

Set theory is concerned with understanding those properties of sets that are independent of the particular elements that make up the sets. Thus the axioms and theorems of set theory apply to all sets in general, whether they are composed of numbers or...

One of the primary features of mathematics is its transformation of the workings of nature into symbolic form. After systematically examining, manipulating and analyzing these abstract symbols, hopefully one may obtain a deeper understanding of the...

Basic mathematical discipline founded by G. Cantor (1845–1918) concerned with the axiomatization of the theory of sets. As a fundamental mathematical and logical discipline set theory, the terminology, and its definitions have found many...

Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its terminology and concepts. These include the operations of union (∪), and intersection...

. It is provable that any class has more subclasses than members. Suppose there were a class of all classes. Its subclasses, being classes, would be members of it. So there can be no class of all classes (and also no greatest cardinal NUMBER, not even...

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Set theory is the mathematical theory of sets, which represent collections of abstract objects. It encompasses the everyday notions, introduced in primary school, often as Venn diagrams, of collections of objects, and the elements of, and membership in,...