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1. REAL NUMBERS

This chapter explores real numbers, focusing on the Fundamental Theorem of Arithmetic and its implications. It establishes that every composite number can be uniquely factored into prime numbers and discusses various applications of this theorem, including the proof of the irrationality of certain numbers. The chapter concludes with exercises and activities designed to reinforce understanding of these concepts.

Sections

  • 1

    Real Numbers

    This section explores fundamental concepts related to real numbers, focusing on the Fundamental Theorem of Arithmetic and the properties of irrational numbers.

    Learning Practice

  • 1.1

    Introduction

    This section introduces the fundamental concepts of real numbers, focusing on the properties of positive integers, including Euclid's division algorithm and the Fundamental Theorem of Arithmetic.

    Learning Practice

  • 1.2

    The Fundamental Theorem Of Arithmetic

    The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of prime numbers.

    Learning Practice

  • 1.3

    Revisiting Irrational Numbers

    This section discusses the nature of irrational numbers, their properties, and proves the irrationality of specific numbers like 2 and 3 using the Fundamental Theorem of Arithmetic.

    Learning Practice

  • 1.4

    Summary

    This section summarizes the key concepts related to the Fundamental Theorem of Arithmetic and its implications in understanding real numbers.

    Learning Practice

References

NCERT Study Material

Class Notes

Memorization

What we have learnt

  • The Fundamental Theorem of ...
  • If a prime number divides t...
  • The chapter provides proofs...

Final Test

Revision Tests

Chapter FAQs