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Mathematical Analysis Fundamentals by Agamirza Bashirov

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Chapter 1

Sets and Proofs

Abstract

Chapter 1 gently introduces the concept of set, operations on sets, and other related definitions. The chapter also includes elements of mathematical logic and basic proof techniques. A special attention is given to the structure of proofs. Relations and functions are defined from general point of view. Two important relations, equivalence and order relations are discussed. The chapter ends with a list of axioms of set theory and some starting implications from them. The proofs in this chapter are given with wide discussions and explanations.

Keywords

Set; proposition; mathematical logic; relation; function; axioms of set theory

Mathematics deals with a great variety of mathematical concepts, each having a precise ...

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