Logical Difficulties With the Modern Theory of Limits - Real Numbers + Limits Math Foundations

Explore the logical challenges in the modern theory of limits in this 36-minute video lecture from the Math Foundations series. Delve into the formal definition of a limit of a sequence, as developed by Bolzano, Cauchy, and Weierstrass. Examine why this definition, despite being considered a cornerstone of modern analysis, faces serious logical issues. Learn about elementary notions of limits, the standard limit definition, and its rewritten form. Follow along with examples to understand the definition's intent and ultimate shortcomings. Suitable for advanced undergraduate-level mathematics students, this lecture provides a critical analysis of fundamental concepts in mathematical analysis.

Introduction
Notions of limit in elementary analysis
The usual definition of "limit"
Rewriting the definition
Finding N
Baby example