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if you shortened your step each time you would never reach it or rather asymptotically reach it which means it will take an infinte amount of time to cover the final infinitely small distance.
Nope , I dont agree
It will not take an infinite amount of time
If you shorten your step each time , the number of steps tend to "infinite " that's true , but the lenght to "zero" thus also the interval of time to cover each step tends to zero
This is the tricky part of the Zeno's paradox
We focus on the term "infinite" , ignoring the term " infinitesim" but both terms must be considered simultanuosly
If so you get a finite result
Zero*infinite = finite ( in some cases)
If the distance if "d" and the speed is "v" the time "t" to reach the target is, according the common sense
t = d / v
A finite value
But you can get the same result also via the Zeno's paradox
Cosider the time t as sum of the partial time : t1,t2,...tn
Where
tn= 1/ 2^n d/v
for n = 1,2,3.....infinite
you have t = d/v( 1/2 + 1/4 + 1/8 + 1/16 + ....)
The number of addendum between the brakets is infinite, nevertheless their sum is : 1
so, again, you get t = d / v
same as common sense would suggest
Obviously I ma talking in principle ,in practice if you try to cover a certain distance using the Zeno's method you will actually take a long time , if not an infinite time, but this has nothing to do with the paradox itself
Last edited by AlbertoT; 09/15/07 10:29.
