Real Numbers and Cauchy Sequences of Rationals - Math Foundations 113

Explore the concept of real numbers and Cauchy sequences in this 30-minute mathematics lecture. Delve into an Archimedean perspective on real numbers, examining nested sequences of intervals with decreasing sizes. Learn how this approach relates to practical applications in approximating quantities. Investigate the Cauchy sequence method for representing real numbers, discussing its advantages and limitations. Cover topics such as the Archimedean definition of real numbers, equality of real numbers, arithmetic operations, infinite decimals, and the Cauchy sequence approach. Gain insights into foundational mathematical concepts and their practical implications in this comprehensive exploration of real number theory.

Introduction
Archimedean definition of real numbers
Two equal real numbers
Arithmetic with 'Archimedean real numbers'
Infinite decimals
Cauchy sequence approach