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!)

Well i can't prove that all even numbers are sum of 2 prime numbers, but i remember my teacher saying that's true last yr i think so i'll take it to be true.

And for the reason why it can't be proved, something to do with integers being infinite maybe and to prove that all even numbers are sum of 2 primes u have to test each of them to show that's the case and since we cant try them all we can't prove it?
Does that make sense? And right now there isn't even a way to find primes efficiently so i guess u can't use anything like induction or what ever other proves are out there to deal with these kinds of problems.

Posted by Steven on 2004-08-22 10:49:02