Achill and the turtle - the soultion

The answer is simply: NO! I am sure this will give the guys at Nike some relief, especially when they plan their tv adds for the olympic summer games. Nevertheless this result is quite astonishing.

You can add numbers and numbers and numbers without stopping and the result will not be that incredible big thing called infinity! This is possible if the numbers that you add are decreasing in the right way. If this happens we say the sum is converging.

The "in the right way" from the sentence above needs some explanation. Actually there are numbers which are decreasing, but their sum is still something REALY BIG. (One example are the numbers 1/2+1/3+1/4+1/5+1/6+... and so on. The numbers are decreasing, but their sum is increasing beyond every limit. REAL BIG THING.)
Luckily, this is different in our race. The numbers are decreasing in the right way. How can we see that? Well, if the part that will be added after a certain point is small, well, then we know at that certain point already what the result will be aproximately. And this means that the sum will not be infinitely big.
In our case this looks like this: After adding 10 + 1 there is "just" 0.1+ 0.01 + 0.001 + ... = 0.11111... missing. After adding 10 + 1 + 0.1 the missing part is just 0.01 +0.001 + ... =0.0111111, which is less then the missing part one addition before. The part that is missing is decreasing with every added number. The sum is converging!

The sum is converging, she is not infinetly big. The value of the sum is simply 11.111111....

After 11,1111... seconds Achill is at the same place where the turtle is and after 12 seconds he gives her and old Zenon a big, fat smile.

......
[diese seite in deutsch]

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