Into The Möbius Labyrinth: Six Möbius Functions, One Nonabelian Machine | Group Theory | Dogmathic
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Into The Möbius Labyrinth: Six Möbius Functions, One Nonabelian Machine | Group Theory | Dogmathic
https://dogmathic.com/ Today we prove a finite set of Möbius transformations forms a group under function composition. We start with the domain A = R {0,1} so every function we use actually maps A to A. Then we define six functions: f(x) = 1/(1-x) g(x) = (x-1)/x h(x) = 1/x i(x) = x j(x) = 1-x k(x) = x/(x-1) From there we check the group axioms ...
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