A rubber band is 1 meter long. An ant starts at one end, crawling at 1 millimeter per second. At the end of each second, the rubber band is instantaneously stretched by an additional meter. (So, at the end of the nth second, the rubber band becomes n+1 meters long.)

Does the ant ever reach the far end of the band? If so, when?

(In reply to Please, find the mistake! by gary)

Actually it is not a mistake. (James Brown, in the 5th comment below came up with the same equation.) If you run the time backward past the start time, and assume the conditions still apply, the ant will be shown to have been be at the "finish line" at that time. The fact that there is no positive time as a root to your equation merely indicates that the time factor will become infinite before (or at best together with) the ant reaching the goal.

Posted by TomM on 2003-02-20 11:36:41