Chapter 01, Real Numbers, Limits and Continuity
Calculus Chapter 01 Real Numbers, Limits and Continuity Notes for Exam Preparation. These calculus notes were created using the most recent BSc/ADS course. We are aware that the BSc math syllabus is extensive and many students are unaware of its completion date. You can now go to Study Medium to access all of the calculus chapters. Because a professional writer created these notes, you can prepare them all without worry.
Both rational and irrational numbers are considered to be real numbers. Real numbers include all rational and irrational numbers, including integers (2, 0, 1), fractions (1/2, 2.5), and the number 3. A function f with variable x is continuous at point “a” on the real line if the limit of f(x), when x approaches the point “a,” is identical to the value of f(x) at “a,” which indicates that f is continuous (a).
Course Contents

Rational numbers, Irrational numbers, Real numbers, Complex numbers

Properties of real numbers, Order properties of R

Absolute value or modules of an R

The completeness property of R

Upper bound, lower bound

Real line, Interval

The working rule for the solution to the inequality

Binary relation (B.R), Domain of B.R, Range of B.R

Function, Onto or surjective function, (11) Function, Bijective Function

Real valued function, Image of a function, Bracket function Finite limit at a finite point

Righthand limit

Lefthand limit
Notes By Prof NaeemUlHaq
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Notes By Imtiaz Hussain
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