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A ball is to be rolled down a 2-mile slope. At the end of the 2-mile slope is a wall. Midway between the 1 mile

and 2 mile points (i.e. 1.5 miles), there's another wall. And midway between the 1 mile and 1.5 mile points (i.e. 1.25 mile), there's another wall. And so on, infinitely. There are infinitely many (impenetrable) walls that get arbitrarily closer and closer to the 1 mile point. But there's no wall at the 1 mile point.

Explain what it means for there to be infinitely (rather than finitely many) walls.

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There are infinitely many wall means that there are a never ending set of walls and cannot be listed by a set of... View the full answer

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