__BASIC SET THEORY__

## 1. INTRODUCTION

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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.

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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.

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