I guess our average forum user has far less experience with complexity of functions and general computer science than I had imagined. The proof of N=NP will be unlikely to have an impact on our actual computation, but merely upon the problems we actually attempt to solve and the ways in which we solve them. In actuality it is a proof that problems whose solutions can be evaluated with polynomial complexity i.e. O(A*n^k) can also be solved with polynomial complexity-- which is to say they vary polynomially with the increase in problem size.
Originally Posted by Oupavoc
You can very easily prove that something is impossible or prove that it is untrue, that is the basis for a very large section of mathematics that you may or may not have run into during your lifetime.
For example, let us take the postulate that
X + Y = 5 for all X and Y less than one million.
This is very clearly not true, as we can rearrange to the following:
X -Y- 5 = 0 for all X and Y less than one million
Allow X and Y to be equal, as allowed by the bounding conditions:
if X = Y, X-Y = 0:
0 - 5 ~= 0
therefore, X+Y ~=5
Substitute ~ for ! if you prefer that as the logical 'NOT' operator.
I am no mathematician, merely an engineer Edited by wcdolphin - 12/27/10 at 11:31am