 Thread: Deeper than primes View Single Post  11th November 2010, 02:05 AM #12296 doronshadmi Penultimate Amazing   Join Date: Mar 2008 Posts: 12,881 epix, you can add Dr. Gérard P. Michon ( http://www.numericana.com/ , http://www.numericana.com/answer/ ) to your "mental cases" list. Quote: http://www.numericana.com/answer/sets.htm#infinity 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.     