u [URL="http://www.youtube.com/watch?v=NDLzyhW6WiA&feature=autoplay&list=PLDA36E5EFA2908F44&index=9&playnext=2"]sa[/URL]y

You have resorted to a tremendous amount of hand-waving, in a sense saying "it is true because I said it is true" or "it is true because I found a sentence on a website that says that I am correct".

You have also cherry-picked from various posts to (poorly) defend some flaws people have pointed out, yet have carefully avoided other posts because you can't defend your proof in light of their contents. Condor and I have both provided those posts to you.

You only "win" because you can't admit defeat. You have had multiple people with college level degrees in math (from Bachelors to Doctorates) tell you that you proof is flawed, even citing specific reasons, but because you don't understand what various mathematical terms mean or what is necessary for a rigorous proof, you refuse to accept what you have been told. There is no indication that you will accept any other PhD telling you the same, regardless of the university with which they are affiliated. You have already insulted everyone on this forum by stating that you are "smarter than the rest of us", you would undoubtedly do the same to any other person who would point out any faults in your proof.

Since Don mentioned Truss and Partington, I found e-mail addresses for them (at Leeds University) and wrote to them this morning. This is the response I got:

[quote]
Dear Prof. Rodenkirch,

It is a long time since we were editors of the Journal of the LMS (1998-2003),
and it is unlikely that we will be able to trace the correspondence for a paper
we rejected at least 8 years ago.

From your message it seems that we rejected the paper on the advice of a
referee who was an expert in the subject (rather than throwing it out immediately
as we would do for obvious "crank" papers). It is quite possible that our referee
did not detect an error in the paper, and made some favourable comments; if
that is the case, but if we did not think the paper was good enough for JLMS,
then we would have rejected the paper and suggested that the author try
elsewhere.

This does not constitute an endorsement of the paper on our part, nor any
claim that it is correct. Any journal wishing to publish the paper must make
its own decision on that matter.

Best regards,
Jonathan Partington
[/quote]

I'm uncertain how he got the impression that I am a professor. I never claimed as such in my e-mail to them.

[QUOTE=rogue;260608]I'm uncertain how he got the impression that I am a professor. I never claimed as such in my e-mail to them.[/QUOTE]

This is a standard practice (at least in mathematics). For example if you go and give a talk in a conference, you will most likely be introduced as a professor even if all the people knew that you are not (or even if they knew that you do not have a Ph.D. etc.). Also, in professional correspondence if the title is not known, you will likely be called a professor.

[QUOTE=Don Blazys;260580]Unlike the rest of you, I [B][I]always[/I][/B] admit it when I make a mistake.
When I wrote...

Quoting myself:
[QUOTE]However, my proof predicts that with four terms, at least
two of them will always have a common factor if w,x,y,z > 2. [/QUOTE]

what I meant to write was w,x,y,z > 3.[/quote]
No, when you make mistakes, you make up something preposterous so you can pretend you didn't. Like you do here. Sorry, Don; but you have now admitted to a second "fatal flaw." In order to make this claim, z=3 has to be "allowed" in your proof.

And are you sure you won't change your mind again when we find a solution for w=x=y=z=4? I'll have to wait till I get back home from a business trip, but I'm sure my program will be able to find one.

[QUOTE=rajula;260609]This is a standard practice (at least in mathematics)[/QUOTE]
Standard practice throughout academia. If you don't know someone's title for certain, always assume something at least as good as they are likely to which they are entitled.

Paul

[QUOTE=Condor;260623]No, when you make mistakes, you make up something preposterous so you can pretend you didn't. Like you do here. Sorry, Don; but you have now admitted to a second "fatal flaw." In order to make this claim, z=3 has to be "allowed" in your proof.

And are you sure you won't change your mind again when we find a solution for w=x=y=z=4? I'll have to wait till I get back home from a business trip, but I'm sure my program will be able to find one.[/QUOTE]

I expect him to eventually conclude that his proof must be true because nobody has found a counter-example.

Quoting "rogue":
[QUOTE]
I expect him to eventually conclude that his proof must be true
because nobody has found a counter-example.
[/QUOTE]
The properties of logarithms clearly preclude the existence of any such
counter-example. Thus, if a counter example did exist, then logarithms
would have to be "scrapped" and eliminated from mathematics entirely!

Quoting "rogue":
[QUOTE]
You have resorted to a tremendous amount of hand-waving.
[/QUOTE]
No, I haven't. It is [B][U]your[/U][/B] arguments that are highly illogical.
Thus, it is [B][I]you[/I][/B] who is doing all the hand waving.

Quoting "rogue":
[QUOTE]
You only "win" because you can't admit defeat.
[/QUOTE]
I [B][I][U]can't[/U][/I][/B] admit to something that isn't true.

The [B][U]truth[/U][/B] is that all your silly arguments have indeed been defeated,
and it is [B][I]your[/I][/B] fragile ego that will not allow [B][I]you[/I][/B] to admit defeat.

[B][U]Because[/U][/B] you have been so easily and soundly defeated, you are angry
and obsessed. That's [B][I]why[/I][/B] you continue to post so incessantly on this
thread while simultaneously crying for it to be locked! :missingteeth:

Quoting "rogue":
[QUOTE]
You have also cherry-picked from various posts to
(poorly) defend some flaws people have pointed out.
[/QUOTE]
Like I said so many times before, if there was even one "fatal flaw"
in my proof, then this thread would have ended a long, [B][I]long[/I][/B] time ago!

As anyone can see, this thread is wildly popular, and I simply don't have
the time to respond to every single comment, so if you really think that
I am "cherry picking" from your comments, then instead of taking all kinds
of silly and meaningless "pot shots" at my proof, why don't you just pick
one and [B][I]only[/I][/B] [B][U]one[/U][/B] issue that you think constitutes some "fatal flaw".

Don.

Misunderstanding n/0 and 0/0: the "fatal flaw"
 

[QUOTE=Don Blazys;260978]why don't you just pick
one and [B][I]only[/I][/B] [B][U]one[/U][/B] issue that you think constitutes some "fatal flaw".[/QUOTE]

OK, here goes.

For nonzero n, n/0 is an undefined division, because of the fact that there is no x such that n/0 = x, lest x * 0 = n != 0 [contradiction]. Think of it this way: x * 0 means we add nothing to itself x times. To paraphrase an old song, nothing plus nothing is nothing. Nothing plus nothing x times is still nothing. x * 0 can never be nonzero. Hence if n is nonzero, there is no x such that x * 0 = n. Ergo, there is no x suitable to define x = n/0. Hence, n/0 must be undefined. It is not allowed. If we see it in the course of solving a problem, we should treat it as a STOP sign, NOT a division problem. Either something has gone wrong in our work, or we will need to resort to taking limits. You seem to (incredibly) agree with this.

But we are not finished.

0/0 is *also* an undefined division, but for a different reason! Suppose I naively (as you do) define 0/0 = n for any n. Well, hey, I think that 0/0 should be pi because pi * 0 = 0. But you might think 0/0 should be 25 because, hey, 25*0 = 0. And the guy down the street might think that 0/0 should be 6. And Mabel from the bowling alley thinks 0/0 should be 73 because that's when she graduated high school. And so on and so on! You might not understand what is happening here, but it is a CRUCIAL idea in mathematics: the idea of well-definedness. Anytime we perform an operation or apply a function in mathematics, we want it to be well-defined, which means among other nifty stuff, that if I calculate f(x) = z, I better get f(x) = z EVERY SINGLE TIME, IN EVERY SINGLE PLACE IN THE UNIVERSE where I calculate f(x)! As a more concrete example, we know that 2+2 = 4 all over the known universe, at all times, in all places, no matter what. Whether we are doing an algebra problem in 6th grade, or launching a rocket to Pluto, 2 + 2 is always 4. Addition is well-defined.

Now consider 0/0. Because n * 0 = 0 for all n, we have a serious problem. 0/0 is most definitely not a well-defined division problem! It has an answer - but it has more than one answer - and that is an infinite number of answers too many. So we must conclude that 0/0 is UNDEFINED, and it too must be treated as a STOP sign, rather than a division problem to be carried out in the usual way.

Note what I am saying carefully. n/0 and 0/0 are not "evil" nor are they "disallowed" nor are they "banished from the earth". Indeed, we find them in mathematics all the time (ask any first-year calculus student). But they cannot be treated as ordinary division problems. It is meaningless to do so. They must be viewed as mathematical STOP signs that require us to pause and rethink our approach to a problem in which they appear.

Note also that n/0 and 0/0 are undefined for two very different reasons. n/0 is undefined because it is nonsensical - there are no numbers that when multiplied by 0 give a nonzero result. Live with it. On the other hand, 0/0 is undefined because it has *too many* answers to choose from - it is not well-defined - and since it would cause problems throughout mathematics even to just pick 0/0 = 1, for instance, we are unable to define 0/0 as a garden-variety division problem.

Don, as you are aware, and have repeatedly appealed to us, the construction of your proof rests on your belief that 0 can divide itself; that is, that there exists n such that 0/0 = n. Unfortunately, because of the above convention regarding 0/0 that is necessarily adopted in mathematics, this is a mistaken belief. Therefore, any "proof" that relies on "0/0 = n" as an underpinning is fatally flawed. You can ask any mathematician from here to the Lucasian Chair. They'll tell you the same thing. In fact, a good third-grade teacher should be able to tell you the same thing.

Sorry, Don, but that's the way it is. Hammering away at the forum with caps lock, colored text, large font, etc. isn't going to change the workings of mathematics, just as shouting at the top of one's lungs won't change the laws of physics when a freight train is bearing down on them.

This forum can be a wonderful resource and you can meet some top mathematicians and interested amateurs, but only if you are willing to respect the subject and your fellow forum members. Please consider becoming a constructive part of our group, rather than yet another banal, sophomoric troll.

Thank you.

[QUOTE=Don Blazys;260978]Like I said so many times before, if there was even one "fatal flaw"
in my proof, then this thread would have ended a long, [B][I]long[/I][/B] time ago![/QUOTE]

You write things like "n*0=0 implies that 0/0 = n" and that "n can be any number". Your hand-waving comes from the fact you say "it is true because that is how I interpret what I read on a website" rather than demonstrating a mathematical understanding of what those statements mean. I (and others) have demonstrated that we understand these things. You have not.

Your hand waving continues when you state that your proof "predicts" other statements without any evidence. It almost appears that you are trying to "induct" other "truths" from your proof for equations with more than three terms. Others have already shown the flaws of that logic. You tend to then "amend" your proof so that "these other conditions must also apply" without stating anything about how you arrived at such conditions.

You have been cherry picking because you have ignored posts 346, 260, 286, and 315 (amongst others).

You have been a troll because you are trying to provoke members by what you write. One example is that you have resorted to insulting every member of this forum because you have been unable to sway anyone to believe that your proof is true. You spend more time attacking members rather than defending your so-called proof.

Is anyone interested in listing the logical fallacies that Don has committed in this thread? I know that some members here are very knowledgeable on the topic of logical fallacies. Granted, I am guilty of some, but not to the same degree.

[QUOTE=Condor;260623]
And are you sure you won't change your mind again when we find a solution for w=x=y=z=4? I'll have to wait till I get back home from a business trip, but I'm sure my program will be able to find one.[/QUOTE]

I missed this post earlier.......

Solutions are already known. In fact, infinitely many are known. Noam
Elkies found the first one. Roger Frye found the smallest positive solution.
[findit it was a non-trivial search]. Solutions are known to be dense in the
rationals.