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Old 11th November 2010, 02:05 AM   #12296
Penultimate Amazing
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Join Date: Mar 2008
Posts: 12,603
epix, you can add Dr. Gérard P. Michon ( , ) to your "mental cases" list.


Grasping Infinity

Mathematicians routinely study things whose infinite versions turn out to be much simpler than the finite ones. One example is the sum (properly called a "series"):

1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256 + ...

This sum is equal to 1-2^-n when carried out only to its n-th term. It's simply equal to 1 if all of the infinitely many terms are added up.

When the ancient Greeks were still wrestling with the concept of infinity, the above sum was underlying something called Zeno's paradox : Before an arrow reaches its target it must first travel half of the distance to it (1/2), then half of what's left (1/4), half of what's left after that (1/8), and so forth. Although there are infinitely many such "steps" the arrow does reach its target... (Try it!)

Last edited by doronshadmi; 11th November 2010 at 02:23 AM.
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