Continuity expresses the property of being uninterrupted. Intuitively, a continuous line or function is one that can be graphed without having to lift the pencil from the paper; there are no missing points, no skipped segments and no disconnections. This intuitive notion of continuity goes back to ancient Greece, where many mathematicians and philosophers believed that reality was a reflection of number. Thus, they thought, since numbers are infinitely divisible, space and time must also be infinitely divisible. In the fifth century B.C., however, the Greek mathematician Zeno pointed out that a number of logical inconsistencies arise when assuming that space is infinitely divisible, and stated his findings in the form of paradoxes. For example, in one paradox Zeno argued that the infinite divisibility of space actually meant that all motion was impossible. His argument went approximately as follows: before reaching any destination a traveler must first...