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     BASIC SET THEORY

1. INTRODUCTION

        Set theory lies at the foundation of all modern mathematics. It gives a very general framework in which almost every branch  of mathematics can be discussed.

        Mathematics have been using sets since the very beginning of the subject. It was realized at the turn of this century that not every collection of elements can be allowed to constitute a set without leading to paradoxes. A paradox is a statement which leads to a logically unacceptable conclusion. One such a famous paradox is due to Russell(1901). In order to avoid such paradoxes, some restrictions have to be put on what one should call sets. These are formulated in various axiom systems for the theory of sets.

 

History

Georg Cantor(1845-1981)

Ernst Zermelo(1871-1953)

Abraham Fraenkel(1891-1965)

Russell's Paradox

Barry's Paradox

Interactive module on Basic Set Theory

                                                                 

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M.Sc. project developed by Ms. Sonali Hande under the guidance of Prof. Inder K. Rana

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