I have seen this before, but for the life of me I cannot understand why the version you give is not differentiable since every term is! Certainly to do with limits of functions and properties not being preserved but my memory is bad.
The embodiment of a "pathological" function, the Weierstrass functions are continuous 𝑒𝑣𝑒𝑟𝑦𝑤𝘩𝑒𝑟𝑒 but differentiable 𝑛𝑜𝑤𝘩𝑒𝑟𝑒pic.twitter.com/yLmONV9pmH
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if you take a derivative all the sudden the series diverges always
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Man I minute ago I read this as "Weird ass" function lol
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Perhaps the first historical fractal!
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Infinitely kinky.
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Reminds me to: f(x)=|x| (f(x)=x if x>=0 and f(x)=-x if x<0) which is continuous everywhere but not differentiable at x=0 but than in its extremes. Or triangle-like and square-like waves as some e.g. 'd Alembert soln of the 1D-wave eqn and Fourier series.
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Like a "continuum" of (logical) ∨'s and ∧'s up and down ;-)pic.twitter.com/Ybj9Ik1nEe
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Do you know Weiestrauss's life? Dropped out of university and became a school teacher, working on mathematics in his spare time, once stayed up all night and missed class - when someone from the school came to check on him he told them to get lost cos he was doing important math
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