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This is known as Zeno's paradox, a series of paradoxes dealing with infinite series of infinitely small components. Here is another:
The Racetrack (or Dichotomy)
One can never reach the end of a racecourse, for in order to do so one would first have to reach the halfway mark, then the halfway mark of the remaining half, then the halfway mark of the final fourth, then of the final eighth, and so on ad infinitum. Since this series of fractions is infinite, one can never hope to get through the entire length of the track (at least not in a finite time).
Start ____________________1/2__________3/4_____7/8__15/16... Finish
Just as one cannot reach the end of the racecourse, one cannot even begin to run. For before one could reach the halfway point, one would have to reach the 1/4 mark, and before that the 1/8 mark, etc., etc. As there is no first point in this series, one can never really get started (this is known as the Reverse Dichotomy).
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