MIT 18.100B Real Analysis, Spring 2025 - Lecture 6: Cauchy Convergence Theorem

4.0 (2)

26 learners

What you'll learn

This course includes

32.5 hours of video
Certificate of completion
Access on mobile and TV

Summary

Keywords

18-100b-real-analysis-spring-2025 bolzano-weierstrass theorem cauchy convergence theorem cauchy sequence continuous at a point contracting map contracting mapping theorem extreme value theorem newton's method x point

Full Transcript

MIT 18.100B Real Analysis, Spring 2025 Instructor: Tobias Holck Colding View the complete course: https://ocw.mit.edu/courses/18-100b-real-analysis-spring-2025/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62Ie7F_tTAhhXoX5_Cl8meG 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.