Real Numbers: Definitions and Equivalence Classes

Related lectures (31)

Page 3 of 4

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

Covers the basics of real analysis, including limits, sequences, and continuous functions.

Explains the Bolzano-Weierstrass Theorem, stating that every bounded sequence has a convergent subsequence.

Covers the concepts of sequences, convergence, and boundedness in mathematics.

Introduces the axiomatic structure of real numbers and their properties, including completeness and the Archimedean property.

Explores real sequences, limits, convergence, divergence, and operations on limits.

Explores Cauchy sequences in real numbers, convergence criteria, and limit definitions.

Explores convergence in Rº, Cauchy sequences, and the Bolzano-Weierstrass theorem.

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

Explains convergence, limits, bounded sequences, and the Bolzano-Weierstrass theorem in real numbers.