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    Zeno's Paradox

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    Suppose that a man wants to cross to the far wall of a room that is 20ft across. First he crosses half of the distance to reach the 10ft mark. Next he crosses halfway across the remaining 10ft to arrive at the 5ft mark. Dividing the distance in half again he crosses to the 2.5ft mark and continues to cross the room in this way dividing each distance in half and crossing to that point because each of the increasingly smaller distances can be divided in half he must reach an infinite number of midpoints in a finite amount of time and will never reach the wall.

    Explain the error in Zeno's Paradox.

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    Solution Preview

    In the Rational parameter set, points have no dimensions-only positions. There are an infinite number of points between A and B. The points A and B are assumed not to move, and the halfway point is presumed to be known and to be exactly halfway between A and B.

    In the Empirical parameter set, however, all points ...

    Solution Summary

    The solution explains the error in Zeno's Paradox.