Gödel proved that there are true sentences that cannot be proved.

Suppose I told you that the Goldbach conjecture is one of those. (The Goldbach conjecture supposes that every even integer number can be expressed as the sum of two odd primes.)

Is that logically possible? (And, no, I haven't proved it!)

There are two distinct problems with this paradox. It is unsolvable because of the numbers ‡ and 0. Like zero, infinity is a number which is neither odd or even. You cannot possibly find the number infinity because it is simply unachievable in classical mathematics. It is in fact a real number, just like zero, but you cannot simply determine whether or not the immense number is odd or even. Infinity is not divisible nor is it changable. ( Infinity * infinity = infinity) (Infinity / infinity = infinity). The same concepts go for zero.  This break in the realm of mathematics causes the paradox to be unsolvable. 

Posted by matt on 2006-08-06 20:34:07