Real Numbers: Properties and Bounds

Related lectures (31)

Page 3 of 4

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

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

Explains the definitions and properties of maximum, minimum, supremum, and infimum in real numbers.

Explores intervals in real numbers, including open and closed intervals, periodic decimals, and irrational numbers.

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

Covers absolute value, density of rationals, and real line topology.

Covers the properties and operations of real numbers, including divisibility rules and the concept of irreducible fractions.

Explores Dedekind cuts in rational numbers, essential for constructing real numbers.

Introduces real analysis basics, including functions, sequences, limits, and set properties in R.

Covers inf/sup, integral part of real numbers, and density of rational numbers.