All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Paradoxes
Provably unprovable? (Posted on 2004-08-22) Difficulty: 4 of 5
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!)

See The Solution Submitted by Federico Kereki    
Rating: 3.2727 (11 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: No problem | Comment 21 of 36 |
(In reply to No problem by Steve Herman)

Yes, you are missing something.  For example, it is not logically possible for the conjecture "there are a finite number of primes" to be true but not provable.  So while SOME conjecture must be true and not provable, it is different to state that a specific conjecture can be true and not provable. 
  Posted by David Shin on 2004-10-15 20:17:45

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (8)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information