Zeno's Paradox

Achilles and the tortoise are having a race! Achilles decides to let the tortoise have a headstart. Who will win the race?

Toggle the "Start the race!" button to make the tortoise run. You control Achilles. Remember, Achilles can't time-warp; if the tortoise is at T₂, Achilles should also be at T₂.

Is it possible for Achilles to ever catch up to the tortoise?

Zeno, a Greek mathematician, thought that Achilles would never be able to catch up. Every time that Achilles reaches the point where the tortoise was, the tortoise has already moved ahead to a new spot!

Another paradox that Zeno introduced was this: a man wants to cross a room. With the first step, he crosses exactly half the distance between himself and the wall. With the next step, he again crosses exactly half the distance between himself and the wall. With each step, he halves the remaining distance between himself and the wall. Can he ever reach the wall?

Chow, S. J. (2006). Zeno's paradoxes and problems with infinity in the physical world. (Order No. MR19456, Dalhousie University (Canada)). ProQuest Dissertations and Theses, 117-117 p. Retrieved from http://search.proquest.com/docview/304952668?accountid=14761. (304952668).

Jenna Jerez, 30 November 2013, Created with GeoGebra