Suppose that the swift Achilles is having a race with a tortoise. Since the tortoise is much slower, she gets a head start. When the tortoise has reached a given point a, Achilles starts. But by the time Achilles reaches a, the tortoise has already moved beyond point a, to point b. And by the time Achilles reaches b the tortoise has already moved a little bit farther along, to point c. Since this process goes on indefinitely, Achilles can never catch up with the tortoise.
How can this be?
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What?! The tortoise actually reached point a? How did he do that, since he would have had to cross 1/2 the distance to point a first... .... .... .... ....
What!? The tortoise...
