What is cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos( cos(…?? // Banach Fixed Point Theorem

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 the Banach Fixed Point Theorem that let's figure out the limit of sequences like this and depends on cos(x) being a so called contractible mapping.

0:00 The sequence
1:17 Cos(x) Graphically
3:25 Spiral Geometric View
7:02 Banach Fixed Point Theorem

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