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Algebra I: A Basic Course in Abstract Algebra by Rajendra Kumar Sharma, Sudesh Kumari Shah, Asha Gauri Shankar

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Chapter 4

Number System

The natural members have been extended to integers, rational numbers, real number etc… This chapter is devoted to the study of natural numbers and integers. The principle of mathematical induction, well ordering principle and their applications are given the greatest common divisor and the congruence relation in integers have also been discussed.

4.1 Number Systems

To count objects we use the numbers 1, 2, 3, … in our daily life. These numbers are called counting numbers. Mathematicians call them natural numbers. An axiomatic approach to study these numbers was given in 1899 by the Italian mathematician Giuseppe Peano. He gave axioms for the study of natural numbers called Peano's Axioms. They are:

Axiom 1. There exists ...

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