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Originally Posted by Shadee  Quote:
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... | Hi Shadee
Sorry I misread your post.... This is not how I understand Zenon's paradox .... it's actually where you get close to the turtle but never reach. It's the sum of half of the differences. The reply below answers my understanding of Zenon's paradox Quote:
Do this seven times and sum the distances.... Achilles has overtaken the turtle..... Now Zenon chose 11 m for his calculation then the calculation does not "allow" Achilles to reach the turtle.
But in reality of the problem, the time associated with Achilles reaching the turtle is also halving. It's like Zenon telling us, you can only take one step towards the turtle and I don't care how you divide up that step!
It goes back to the series of numbers 1/1, 1/2, 1/4, 1/8, 1/16 .....the sum of which approach the value of two but never quite gets there. We are adding an infinite number of numbers, but they are are getting infinitely smaller.
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Last edited by romansh : 03-16-2008 at 10:47 PM.
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