Using The Banach Fixed Point

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This weird expression of taking cos over and over again is just a sequence x_n=cos(x_{n-1}). There is a very cool theorem called ...

This video highlights the fascinating world of metric spaces

My video on Sesame Studios: https://www.youtube.com/watch?v=BTjAiyyG2sw The Curiosity Box by Vsauce: ...

We explore

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16.1 The

In this video, I prove the celebrated

In this video, I proved the existence but not uniqueness of a

Please note that Patrick recaps the last lecture near the start and you may want to pause those slides. You can find that lecture ...

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Fixed Point

This video looks at an intriguing equation as an excuse to introduct the Contraction Mapping Theorem, a fascinating theorem that ...