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 Zeno’s paradox, is named after the mathematician Zeno, born about 496 B.C. in Italy. According to Zeno’s paradox, suppose Achilles starts out 1 meter behind a tortoise. Also, suppose Achilles walks 10 times as fast as the tortoise crawls. When Achilles reaches the point where the tortoise started, the tortoise is 1/10 of a meter ahead of Achilles; when Achilles 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, Achilles 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 Achilles ever pass the tortoise?