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A naive theory in the sense of "naive set theory" is a non-formalized theory, that is, a theory that uses natural language to describe sets and operations on sets. Such theory treats sets as platonic absolute objects. The words and, or, if ... then, not, for some, for every are treated as in ordinary mathematics.
Apr 10, 2007 · The Early Development of Set Theory. First published Tue Apr 10, 2007; substantive revision Mon Oct 7, 2024. Set theory is one of the greatest achievements of modern mathematics. Basically all mathematical concepts, methods, and results admit of representation within axiomatic set theory. Thus set theory has served quite a unique role by ...
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory — as a branch of mathematics — is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was ...
Jul 24, 2024 · Set theory, a fundamental branch of mathematics that deals with the study of sets, or collections of objects, has evolved significantly since its inception. It provides the foundation for various…
Sep 20, 2024 · By 1900, set theory was recognized as a distinct branch of mathematics. At just that time, however, several contradictions in so-called naive set theory were discovered. In order to eliminate such problems, an axiomatic basis was developed for the theory of sets analogous to that developed for elementary geometry.
Nov 7, 2024 · A branch of mathematics which attempts to formalize the nature of the set using a minimal collection of independent axioms. Unfortunately, as discovered by its earliest proponents, naive set theory quickly runs into a number of paradoxes (such as Russell's antinomy), so a less sweeping and more formal theory known as axiomatic set theory must be used.
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It is apparent that much of what mathematicians study is tied to set theory. Georg Cantor(pictured left) is considered the founder of Set Theory as a branch of study in mathematics. Around 1870, Cantor developed the theory of infinite series and the related analysis of it, shaping the future of the study of set theory.
