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Aristotle's wheel paradox

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1 hour ago, Darrell Hougen said:

Now, assume that the interval, [0, 2] contains N points.

That is of course the fallacy. The interval [0,2] contains infinitely many points, and infinity is not a natural number, therefore the notion of density doesn't work, as the density is also infinite, and 2 =  ∞. Cantor, cardinality, continuum and all that. It isn't surprising that people like Aristotle and Galileo didn't understand such things well. Therefore those helpless attempts to consider circles "jumping" or "waiting" to make up for differences in traveled distance in Aristotle's paradox.

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