As the story goes, Prometheus stole fire from the gods of Olympus and gave it to humans. This made Zeus very angry. Prometheus was told to return the fire by 1:00pm, an order that he defied.

To punish Prometheus for his disobedience, at 1:00 pm, Zeus paused time (he can do this as a god), and conjured up an infinite number of demons. To the first demon he said:
"If Prometheus is still alive at 2:00 pm, kill him!" To the second one he said:
"If Prometheus is still alive at 1:30 pm, kill him!" And to the third:
"If Prometheus is still alive at 1:15 pm, kill him!"

So he kept ordering each of his demons to kill Prometheus in half the time of the demon before. After giving orders to all the demons, Zeus un-paused time again and waited.

At two o'clock, Prometheus was dead, and the council of gods was none too happy about it. They told Zeus:
"Tell us which one of your demons killed Prometheus, so that we may punish him!"

"But none of my demons could possibly have killed Prometheus!" answered Zeus. How can this be?

based from sequences and series:
the times the demons were supposed to kill kept getting cut in half, so we take 1/2^1 + 1/2^2 + ..., getting 1/2 + 1/4 + 1/8 + 1/16 +... which converges to 2 when 1/2^n where n = infinity
therefore, no demon killed him because the times only approximate 2 but never exactly reach it
mathematically it has to converge to 2, which is why for the problem they picked 2 o'clock to make the riddle work out. since it converges to two, you are taking the limit, so no demon actually killed him

Posted by carolyn on 2002-08-27 12:23:37