There are a number of paradoxes associated with infinite sets and the concept of
ID: 3199529 • Letter: T
Question
There are a number of paradoxes associated with infinite sets and the concept of infinity. Once of these called Zeno's Paradox is named after the mathematician Zeno, born about 496 B.C. in Italy. According to Zeno's paradox, suppose Achelles starts out 1 meter behind a tortoise. Also suppose that Achelles walked 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 Zeno's Paradox, Achelles gets closer and closer to the tortoise but never catches up to the tortoise. Address the following: Do you believe the reasoning process is sound? Explain why/why not. In actuality, if this situation were real, would Achelles ever pass the tortoise.
Explanation / Answer
a) The reasoning process is sound
Achelles is walking 10 times faster than the tortoise, so when Achelles reaches the first point where tortoise was present, tortoise has moved by a distance of 1/10m, similarly when achelles reaches the next point, the tortoise would have moved further by 1/100m distance.
Hence the distance between achelles and tortoise after each round is given by the set
S = {1/10,1/100,1/1000,1/10000,....}
This will be an infinite process
b)
If the situation is real, then the Achelles will never be able to pass the tortoise, he will reach almost close to the tortoise after n iterations where n tends to infinity, but he will still be behind the tortoise
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