| The sum of a geometric series is 1 + x + x2 + x3 + x4 + ... = 1/(1 - x) if |x| < 1. If we use this formula without checking x is small, then we can get nonsense like 1 + 2 + 4 + 8 + 16 + ... = 1/(1-2) = -1. Or is it nonsense? We'll look at number systems where this computation actually works, and we'll derive some of the remarkable properties of those mathematical worlds, even drawing (fractal-like) pictures of them. | ||
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