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The Devil's Staircase is similar to Zeno's Paradox. There is no paradox. You are only looking at the problem in the wrong way. The slope of the Cantor's Function is not zero. If it was exactly zero then you could never get from 0 to 1 vertically. Thus, the slope of Cantor's Function approaches zero, but it is never exactly zero. This means Cantor's Function climbs vertically at an infinitesimal pace.