There are a number of paradoxes (a statement that appears
Chapter 2, Problem 2.1.419(choose chapter or problem)
There are a number of paradoxes (a statement that appears to be true and false at the same time) associated with infinite sets and the concept of infinity. One of these, called Zenos Paradox, is named after the mathematician Zeno, born about 496 b.c. in Italy. According to Zenos paradox, suppose Achelles starts out 1 meter behind a tortoise. Also, suppose Achelles walks 10 times as fast as the tortoise crawls. When Achelles reaches the point where the tortoise started, the tortoise is 1/10 of a meter ahead of Achelles; when Achelles reaches the point where the tortoise was 1/10 of a meter ahead, the tortoise is now 1/100 of a meter ahead; and so on. According to Zenos Paradox, Achelles gets closer and closer to the tortoise but never catches up to the tortoise. a) Do you believe the reasoning process is sound? If not, explain why not. b) In actuality, if this situation were real, would Achelles ever pass the tortoise?
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