Dispelling Limit Confusions in Pure Mathematics - Three Types of Series Limits

Explore the complexities of limits in pure mathematics through this 25-minute lecture that challenges common misconceptions. Delve into the three distinct types of limiting behavior in infinite series, with a focus on the Cauchy condition's significance. Examine the process of converting series to sequences, understand the limits of series and sequences, and critically analyze the convergence of Cauchy sequences. Uncover the controversial practice of creating limits without proper justification, gaining valuable insights into the often-overlooked intricacies of mathematical analysis.

Three kinds of limits for series
Converting a series to a sequence
Limit of a series/sequence
The Cauchy condition
False fact re convergence of Cauchy sequences
The big cheat: creating limits out of thin air