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Sorry, but I find it much easier to find a function with your property, compared to the continuous everywhere but differentiable nowhere functions. In fact, he
by frotaur 2y ago
Sorry, but I find it much easier to find a function with your property, compared to the continuous everywhere but differentiable nowhere functions.
In fact, here is an uncountable family of them :
f(x) = x^2 * rand(0,1)
Where rand(0,1) is a uniform number between 0 and 1, sampled for every x.
- seanhunter 2y agoIntroducing a stochastic function is cheating. You expect calculus to break if you just throw in stochastic functions willy-nilly, so that doesn’t challenge my intuition at all.
- Someone 2y agoSome of those are continuous and differentiable everywhere. Examples: f(x) = 0 f(x) = ½ x² Also: doesn’t the claim that you can pick such a function require an extreme version of the axiom of choice, where you claim you can pick an element of each set in a set of sets that has uncountably many items?