i say fog, cannot die, because its not alive, other than that i say vampire, but that is just irrational

This might be a paradox mathematically, but in real life you could use it to work out the point at which he passes the tortoise (to the desired decimal places)

At your first "point" achiles is 10 feet behind, (100 from start)
then 1 foot behind (110 from start)
then 1/10th of a foot behind (111 feet from start)

So to the nearest foot, achiles would pass the tortoise at 111 feet. In reality it would be just after 111feet, but you can be 100% sure that if the race was 112 feet long, Achiles would win.

How about an endless cycle?

Say that you have a box. Within the box contains the entire universe. So within the box, there is a box with the universe and that has a box in it and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box and that has a box etc.

^Like on futurama

dtewi, nice way of putting it, ima read up on paradoxes now, intriguing

Whoa, I'm doing the same thing. Reading up on them

Yes TWRoO. That's were I got it from. "The Farnsworth Paradox"

Dang, people got here before me who understand what's going on. It's not a paradox anymore so that .333... x 3 = 1. The real issue is that people don't understand infinity. They can't fathom reaching it, and thus problems like this are a real issue. Achilles overtakes the tortoise after an infinite amount of these little repetitions. Although it's hard for us to imagine reaching infinity, doing so is not impossible. Thus, there's no paradox. So he must reach infinity to pass the tortoise, but so what? We overtake an infinite amount of points with each and every step. Just because we can't imagine it doesn't mean it isn't possible.

Edit: In case that wasn't clear, I was saying there is no mathematical paradox.  People just can't imagine reaching infinity well.