@paulg brevity and, thus, wit.
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@paulg Trivially, x = x + 0 + 0 + 0 + ... . I'm guessing you mean with a meaningful infinite series; but then what's "meaningful"? -
@paulg Probably the most useful answer here comes from Kolmogorov complexity: Can the terms of the series somehow be described succinctly? -
@paulg In that case the answer is that with probability 1, a Real chosen uniformly at random from [0, 1) has no series w/ finite complexity. - 1 more reply
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@paulg Weierstrass theorem says you can approximate anything with an infinite series of polynomsThanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg yes, last digit of piThanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg Let f be defined by f(x) = 1 if x is rational and f(x) = 0 if x is irrational. f is discontinuous at every point x.Thanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg If you restrict yourself to only ℝ, all real numbers can be approximated with infinite series.Thanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg my IP addressThanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg Yes. Here is an example https://en.m.wikipedia.org/wiki/Non-analytic_smooth_function …Thanks. Twitter will use this to make your timeline better. UndoUndo
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@paulg Circular reasoningThanks. Twitter will use this to make your timeline better. UndoUndo
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