Real Numbers as Cauchy Sequences - Limitations and Challenges - Math Foundations 114

Explore the logical weaknesses in using Cauchy sequences as a foundation for real number theory in this 52-minute video lecture. Delve into topics such as infinite sequences of rationals, choice and algorithmic approaches to infinite sequences, ambiguities in Cauchy requirements and equivalence classes, and the implications for rational numbers. Examine the problems with "Cauchy sequence real numbers" through detailed explanations and examples. Gain critical insights into the foundations of mathematics and challenge conventional understanding of real number theory.

Intro to the problems with "Cauchy sequence real numbers"
Infinite sequences of rationals
Choice approach to infinite sequences
Algorithmic approach to infinite sequences
Cauchy requirement is ambiguous
Algorithmically generated infinite sequences
Equivalence classes are ambiguous
Two Cauchy sequences of rationals
What is an 'equivalence class'?
Algorithmic approach to sequences
Applications and infinite decimals
Show the arithmetic!
What happens to rational numbers?