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Any two functions when glued together as a piecewise function can have a discontinuity, that's true, but that’s not what this is... this is a sequence with a recursive term. Sort of like the fibonacci sequence where a term is defined by the one preceding it, so you have to, conceptually, computer all the way down to the base case. It just so happens that the rule in this article for some reason becomes very well ordered past a certain step when you plot the values, at least to our human brains.

The numberphile video to which the article links is a good watch!




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