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Zeno formulated several mind-boggling questions, ''Zeno's paradoxes.'' They were a challenge to philosophers. For the most part, today they are considered to have been solved by the mathematical concept known as the ''limit.''

Zeno formulated several mind-boggling questions, ''Zeno's paradoxes.'' They were a challenge to philosophers. For the most part, today they are considered to have been solved by the mathematical concept known as the ''limit.''

One of Zeno's paradoxes claims that it is impossible ever to reach a destination, such as a house that is a mile away. For in order to walk that mile, you must first walk half a mile, leaving half a mile to go. But before you can complete that remaining half a mile, you must first walk a quarter of a mile, leaving a quarter of a mile to go... and so on. Thus, apparently, you can get closer and closer and closer to your destination but can never actually quite get there.

One of Zeno's paradoxes claims that it is impossible ever to reach a destination, such as a house that is a mile away. For in order to walk that mile, you must first walk half a mile, leaving half a mile to go. But before you can complete that remaining half a mile, you must first walk a quarter of a mile, leaving a quarter of a mile to go... and so on. Thus, apparently, you can get closer and closer and closer to your destination but can never actually quite get there. 

 

The solution is that the time it takes to make each partial step approaches zero as the number of steps approaches infinity, and they cancel each other out.