Moving in Frames!?!?

[Namloh2000]

okay, so let's say I ran 3 miles. At one point, I must have been halfway between start and finish right? From the halfway point, I must have existed halfway from there and the remaining 1.5 miles also. And halfway between THAT point and the finish. Then halfway from THAT point and the finish. I must have existed at all these halfway points, but if motion was fluid, couldn't this not be accomplished, being that I can devide my new remaining distance in half from here to infinity, meaning that I would have to be running forever? The implications are staggering!

seriously though, what's up - how come I can run 3 miles?

[recon]

This is known as Zeno's Paradox. The sum of an infinite series is still finite. Google it. Much has been said about it.

[Namloh2000]

okay so i read up a bit and the solution seems to be something in that because the sum of the series ½ + ¼ + 1/8 + ... is equal to 1. The total time is finite because each step is done in half as much time as the previous step.

But I still don't understand.

[recon]

OK, I see that you don't have much faith in mathematics. Anyway, go visit here if you are interested: http://www.physicsforums.com/showthread.php?t=22419

You can open a new thread in the General Math section if you still don't believe in Zeno's Paradox. You will get more replies there, and most of them will be harsh. So good luck! :)