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. Check out my MATH MERCH line in collaboration with Beautiful Equations ► 0:00 The sequence 1:17 Cos(x) Graphically 3:25 Spiral Geometric View 7:02 Banach Fixed Point Theorem COURSE PLAYLISTS: ►DISCRETE MATH: ►LINEAR ALGEBRA: ►CALCULUS I: ► CALCULUS II: ►MULTIVARIABLE CALCULUS (Calc III):