MIT 18.100A Real Analysis, Fall 2020 - Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function

MIT 18.100A Real Analysis, Fall 2020 Instructor: Dr. Casey Rodriguez View the complete course: http://ocw.mit.edu/courses/18-100a-real-analysis-fall-2020/ YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP61O7HkcF7UImpM0cR_L2gSw We can show that differentiability implies continuity, but does continuity imply differentiability? We use the continuity and oscillatory nature of sine and cosine to prove the existence of Weierstrass’ continuous but nowhere differentiable function. 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.