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Chapter 01: Real numbers, limits and continuity

Homogeneous discontinuous function

Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. The notes of this chapter is written by Prof. Muhammad Farooq, Punjab College, Sargodha.

Contents and summary

  • Articles of Exercise 1.1
    • Rational numbers, Irrational numbers, Real numbers, Complex numbers
    • Properties of real numbers, Order properties of $\mathbb{R}$
    • Absolute value or modules of a $\mathbb{R}$
    • The completeness property of $\mathbb{R}$
    • Upper bound, lower bound
    • Real line, Interval
    • Working rule for the solution of inequality
    • Binary relation (B.R), Domain of B.R, Range of B.R
    • Function, Onto or surjective funiton, (1-1) Function, Bijective Function
    • Real valued function, Image of a function, Bracket function
  • Articles of Exercise 1.2
    • Finite limit at a finite point
    • Left hand limit
    • Right hand limit
  • Articles of Exercise 1.3
    • Continuity

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