While not strictly a supertask, this idea has inspired many papers about supertasks. A man called Prometheus angers Zeus, so Zeus gathers an infinite number of demons and issues them with the following commands. Demon 1: if Prometheus is not dead in one hour kill him, Demon 2: if Prometheus is not dead in half an hour kill him, Demon 3: if Prometheus is not dead in quarter of an hour kill him, and so on. As it turns out Prometheus was dead within the hour (as he didn’t really have much chance). The council of gods was not happy about this and pressed Zeus on the point. But none of his demons could be found guilty, as, for each positive integer n, it was not possible for the nth demon to have killed Prometheus because the (n + 1) th demon should already have done so. Similar paradoxes involving a man trying to walk a mile from A to B but the demons building a wall in front of him if he reaches 1/2, 1/4, 1/8, … of a mile past A, so he hits some sort of invisible barrier when he reaches A even though no wall has been built.
26 February 2008