[clarknova]

Originally Posted by HarryT

Spoiler:

OK, but suppose the track was increasing in length by 1km every 10m. Would he still finish? Can you show that he'll finish no matter what the length increase is?

Spoiler:

Of course he wouldn't finish. You've forgotten that this isn't just a math problem. Achilles would never finish that, as he has a Trojan war to fight and die in.

It's feasible for him to waste 3 and a half hours on this crap for the gods' amusement, but he couldn't spend the millennia eons it would take to finish the race you created above. Even if he wasn't needed for historic wars, people (even Greek Heroes) just don't live long enough to finish that race.

Though perhaps that race could be done as some sort of hellish torture in Hades or Tartarus...

Edit: Millennia doesn't quite describe it. After about 2,315 years of constant running Achilles would only be 35% done, and the track now stretches 488 Astronomical Units. I'm not even sure my computer could finish this race at over 2^24 times the speed of Achilles.