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Originally Posted by romansh  OK .... so using the example I gave and 11.1 m, Achilles catches up even if you continually split the difference in half. |
You don't split the difference in half, you split the distance he has to travel in half and you keep doing that. So using your distance, to travel 11.1 m he first has to pass the halfway point at some point which is 5.55 m, but to travel 5.55 m he fist has to pass the halfway point of that which is 2.775 m but to travel 2.775 m he first has to pass the halfway point of that distance at some point which is 1.3875 m... see where I'm going with this? It goes on forever when you realize that every number except 0 can be divided into new numbers endlessly.
Whether or not he catches up with the turtle isn't what the paradox was about. He's explained the paradox in a different scenario too where there's no race involved but just a frog on one side of a pond which has to cross the pond by jumping from one lilly pad to the next. Between each lilly pad there's another lilly pad right inbetween the two (also between the first one and the one that's between the first and second one etc etc). The question in this case is will the frog ever make it to the other side of the pond. Which of course is no because in that scenario there's an infinite number of lillypads just like the infinite number of halfway points Achilles has to traverse in theory.