Construction of the real numbers

Related lectures (31)

Page 3 of 4

Covers the organization of real numbers, axioms, and bounds, including infimum and supremum.

Covers the Archimedean property and the proposition for all x in a set, there exists a positive real number n such that n*x is greater than y.

Explores boundaries in sets, defining them as points not well separated from the set or its complement.

Covers the definition and properties of whole number powers, including examples and proofs.

Introduces functions with real values, derivatives, and the Jacobian matrix, along with compound functions and variable change applications.

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Discusses Cauchy sequences, sub-sequences, and numerical series with parameters.

Covers sequences defined by recurrence, with examples and step-by-step demonstrations.

Explains infinite branches, vertical and oblique asymptotes, and limit calculations for functions with square roots.

Covers the definition and basic properties of the absolute value function for real numbers.