Well you're only seeing this from the space perspective, you need to consider time also. Over time Achilles will be closer and closer to the tortoise, adding distances that are getting smaller, but you know that infinite sums can lead to a not infinite result. When you compare space over time (or velocity) of the 2 subjects you'll see that Achilles is going faster, and will eventually pass the tortoise.

dtewi.. can't you do your own homework???

"Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise."

This assumption is wrong because Achilles is moving at a faster pace than the tortoise. If Achilles reached the 100 mark when the tortoise reached 10 ahead, then Achilles is moving at a much faster, constant speed. Achilles will have to pass the tortoise because he is moving faster than the tortoise at a constant rate.

The paradox is not saying an infinte distance. It is saying he needs to travel a finite distance that have an infinite number of points.

A finite distance can be reached, but an infinite amount can not.

@Dtewi - Another way to use this paradox. If I want to move 100 feet, I have to move 50 feet first. If I want to move 50, I have to move 25 first. And it goes on and on and on. So, whatever distance I want to move, I have to move half that first, so I´m stuck. Paradox.

The infinite number of points is not true. We could count them if we could slow time down and watch. Since he is moving faster, at the point that he is dead level with the tortoise, he has just passed all "infinite" points. The only thing left is for the tortoise to do the same to him. The points are directly related to distance, again finite. So this paradox is only a paradox from an abstract/philosophical standpoint.

Just for clarification, I just copied the article from Wikipedia.

I didn't write it, I just wanted to see what other people would say about it.

@ marcio

I believe that is the Dichotomy Paradox.

@ luinil

You seem to be ignoring the concept of infinity.

For Achilles to pass, he has to reach infinity. Infinity can not possibly be reached, so how can he pass?

Exactly. That´s math for you.

You´re right. I knew this paradox, but I didn´t know its name.