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What is Continuity? According to a Mathematician.
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What is continuity and what is the popcorn function? From primitive notions to the modern day, there have been a variety of attempts at understanding continuity and functions. We talk about them here, in this video.
(This video was sponsored by Brilliant)
//Articles
A Study of Maurice Fréchet: I. His Early Work on Point Set Theory and the Theory of Functionals
Angus E. Taylor
//Books
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Real Analysis:
Control Theory:
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DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 Start
0:55 Intuitive Continuity
2:39 Something is wrong with Power Series
3:41 Making Popcorn in MATLAB
5:33 Frechet and his Metric Spaces
7:10 Making popcorn... no really
10:15 Continuity in Metric Spaces
11:10 Discontinuity of the Popcorn Function
12:23 Topology was STOLEN!
14:26 Continuity of the Popcorn Function
15:27 The last words on Continuity
(This video was sponsored by Brilliant)
//Articles
A Study of Maurice Fréchet: I. His Early Work on Point Set Theory and the Theory of Functionals
Angus E. Taylor
//Books
//Watch Next
Real Analysis:
Control Theory:
//Music Provided by Epidemic Sound
Use this referral link to get a 30 day free trial with Epidemic Sound for your YouTube channel:
//Recording Equipment
DISCLAIMER: The links above in this description may be affiliate links. If you make a purchase with the links provided I may receive a small commission, but with no additional charge to you :) Thank you for supporting my channel so that I can continue to produce mathematics content for you!
0:00 Start
0:55 Intuitive Continuity
2:39 Something is wrong with Power Series
3:41 Making Popcorn in MATLAB
5:33 Frechet and his Metric Spaces
7:10 Making popcorn... no really
10:15 Continuity in Metric Spaces
11:10 Discontinuity of the Popcorn Function
12:23 Topology was STOLEN!
14:26 Continuity of the Popcorn Function
15:27 The last words on Continuity
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