Real Numbers: Definitions and Properties

Related lectures (32)

Explores the conditions for continuity of a function on real numbers.

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

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

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

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.

Introduces the properties and structure of real numbers, emphasizing completeness and the Archimedean property.

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 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 the properties and applications of roots of real numbers through practical examples.

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

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