Lectures related to Introduction to Real Numbers

Introduces equivalence relations, partitions, partial orderings, and total ordering concepts with examples and definitions.

Explores real numbers, focusing on the square root of 2 and the implications of its irrationality.

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

Explains the concept of infimum in real numbers and its properties.

Covers the existence of real numbers and equivalence classes of Cauchy sequences.

Covers the basics of real analysis, including functions, limits, and max/min functions.

Explores the equivalence of inequalities to determine the least upper bound of a set.

Covers minimum, maximum, infimum, and supremum concepts in real numbers with examples and proofs.

Explores the limit of a sequence, convergence conditions, algebraic operations, and order relations.

Introduces the course content by linking familiar mathematics with upcoming topics.