Posted on 08/14/2010 7:57:39 PM PDT by LibWhacker
Initially hailed as a solution to the biggest question in computer science, the latest attempt to prove P ≠ NP – otherwise known as the "P vs NP" problem – seems to be running into trouble.
Two prominent computer scientists have pointed out potentially "fatal flaws" in the draft proof by Vinay Deolalikar of Hewlett-Packard Labs in Palo Alto, California.
Since the 100-page proof exploded onto the internet a week ago, mathematicians and computer scientists have been racing to make sense of it.
The problem concerns the speed at which a computer can accomplish a task such as factorising a number. Roughly speaking, P is the set of problems that can be computed quickly, while NP contains problems for which the answer can be checked quickly. Serious hole?
It is generally suspected that P ≠ NP. If this is so, it would impose severe limits on what computers can accomplish. Deolalikar claims to have proved this. If he turns out to be correct, he will earn himself a $1 million Millennium prize from the Clay Mathematics Institute in Cambridge, Massachusetts.
(Excerpt) Read more at newscientist.com ...
No, by definition, it is not. Even Numbers are defined as numbers >1, and divisible by 2.
By extension, that now includes the numeri ficti - {-2,-4,-6...}
0 is excluded.
Isn’t that what I just said...?!
That’s a different equation to my literal mind. If P is 0 and NP is any other number than 0, then P can only equal NP if other equations are applied, which is more than the stated equation asks for. Then again, I’m not even a math amateur.
If you’re right, where’s your million plus a bonus for your less than a page answer?!
Dr. Math says 0 is even.
http://mathforum.org/library/drmath/view/57132.html
Who am I to argue with this?
I forgot to thank you for the brain exercise!
Now, now... Stop that! You’ll confuse people. Zero is even. Negative numbers aren’t fictional. And you can’t divide by zero. lol
I am not right - clearly, 0<>1.
The proof is a trick. Meant to be a joke.
LOL - what, nobody gets my humor, today...
Did you know that pie are not square? But 2 pie are.
“Thus, (A+B)(A-B)=B(A-B)
Therefore, it should be obvious to the casual observer, that A+B=B”
You’d be right if division by zero were permitted. Unfortunately it’s not, QED, you’re wrong.
LOL! I never was all that good at math!
Dunno who you are, but the good Dr’s are wrong. See the Peano Axioms, and go from there.
I meant to be wrong.
Apropos, one of my favorite HS teachers - Rocky, aka MR. Rockwell, aka the math guy - died last week.
He was a vet, a pilot, and a really good influence on my life. Looked at me funny when I enlisted during the Iranian Hostage Crises, but was really supportive.
I kept meaning to go show him my degree in Math - it would have made him laugh.
But I never did.
Sigh.
Dunno who you are, but Dr. Penner isn’t buying your story:
^ Lemma B.2.2, The integer 0 is even and is not odd, in Penner, Robert C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific. pp. 34. ISBN 9810240880.
“I meant to be wrong.”
I assumed so. One of my favorite HS teachers taught us the fallacy underlying this “proof.” But until he did so, it had us all baffled.
Okay, now I’m worried; I understand at least part of the concept.
Nothing yet, but if someone does send me a million dollars that I didn’t earn, all refunds are subject to a 99% service fee. : )
Well, clearly, Dr. Penner wrote his discrete maths text after I graduated. LOL.
And yes, Rocky was the one who showed my the silly 1=0 trick.
Divergence, divergence, hmmm...
Or, as Rocky used to put it, 1=2, but only for very large values of 1!
“Did you know that pie are not square? But 2 pie are.”
OK... that I got. LOL
;)
Silly wabbit, math is for twicks!
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.