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Home/Calculus/Chapter 1
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Chapter 1
Available

Real Numbers and Functions

Build a solid foundation for calculus by mastering set theory, real number construction, and essential function properties

4 Courses
12-15 Hours
Foundation Level

What You'll Learn

Rigorous mathematical foundations for calculus
Step-by-step proofs and worked examples
Interactive practice quizzes for each topic
Prerequisites for limits and continuity

Courses in This Chapter

Course 1
Set Theory Foundations
Master the language of mathematics: sets, operations, De Morgan's laws, and countability concepts
3-4 hours
Set Definitions & Notation
Set Operations
De Morgan's Laws
Countable vs Uncountable Sets
Course 2
Real Number Construction
Understand how real numbers are rigorously constructed using Dedekind cuts and the completeness axiom
3-4 hours
Rational Number Gaps
Dedekind Cuts
Real Number Axioms
Completeness Property
Course 3
Properties of Real Numbers
Explore absolute value, bounded sets, supremum/infimum, and fundamental inequalities
3-4 hours
Absolute Value Properties
Bounded Sets
Supremum & Infimum
AM-GM & Cauchy-Schwarz
Course 4
Functions Fundamentals
Study function properties: boundedness, monotonicity, periodicity, and special functions
3-4 hours
Bounded Functions
Monotonic Functions
Periodic Functions
Special Functions