Lecture 6: Cauchy Convergence Theorem
MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-r... YouTube Playlist: • MIT 18.100B Real Analysis, Spring 2025 In this lecture we show that there is way to determine whether or not a sequence is convergent even if we are unable to write down explicitly the limit. This is the notion of a sequence being a Cauchy sequence and has wide ranging applications. We will also discuss some of these applications. License: Creative Commons BY-NC-SA More information at https://ocw.mit.edu/terms More courses at https://ocw.mit.edu Support OCW at http://ow.ly/a1If50zVRlQ We encourage constructive comments and discussion on OCW’s YouTube and other social media channels. Personal attacks, hate speech, trolling, and inappropriate comments are not allowed and may be removed. More details at https://ocw.mit.edu/comments.

Lecture 7: Bolzano–Weierstrass Theorem; Cauchy Sequences; Series

Lecture 1: Introduction to Real Numbers

Vector Spaces 1

The Man Who Worked At Subway, Then Solved An "Impossible" Problem

Lecture 8: Convergence Tests for Series; Power Series

Intro to Cauchy Sequences and Cauchy Criterion | Real Analysis

Lecture 1: Introduction to China's History

Terence Tao on Grigori Perelman solving Poincare Conjecture | Lex Fridman Podcast Clips

The Concept So Much of Modern Math is Built On | Compactness

Lecture 10: Continuous Functions; Exponential Function (cont.)

The Hardest Questions in Physics | World Science Festival

Real Analysis | Cauchy Sequences

Conversation: Salam, Sciama, Witten and Budinich

But what is a Laplace Transform?

Lecture 13: Portfolio Management

Sarah Paine - Why Putin and Xi can't escape geography

"First Proof: Mathematicians Putting AI to the Test" March 14, 2026

Lecture 2: Introduction to Real Numbers (cont.)

