Lectures related to Real Numbers: Order and Completeness

Explains the concepts of open and closed sets in real numbers.

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

Covers solutions to true/false questions on subsets, upper bounds, real numbers, and set properties.

Covers the structure and properties of real numbers, including the introduction to the axiomatic system and the implications of Archimedean property.

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

Introduces real number sequences, limits, and their properties.

Covers the concept of supremum in real numbers and its properties as the least upper bound of a set.

Illustrates the calculation of infimum and supremum for a set of elements.

Explores interior points, closures, and set properties in real analysis.

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