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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Mon Dec 21, 2009 5:51 pm Post subject: |
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Kemo you said it yourself "If it is indeed a proof mathematicians would recognize it" Therefore Jeffjo is no mathematician
QED Just another asshole wanna be. _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Mon Dec 21, 2009 9:48 pm Post subject: |
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| bill wrote: | | Kemo you said it yourself "If it is indeed a proof mathematicians would recognize it" Therefore Jeffjo is no mathematician . |
Problem is, it isn't a proof. ANd you have great difficulty applying logical statements, like "If A then B." |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Mon Dec 21, 2009 10:11 pm Post subject: |
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Then how come the PhD I sent it to said otherwise. I received a letter from the mathematical association of America for my contributions to math. Especially My law of algebraic consistency. Since you were interested in math I thought I would help you out by showing you something new. But all you can do Jeffjo is jump to conclusions because you do not understand what I am trying to show you. So Jeffjo since I have been called to active duty I will not have time to play with you and Rob. _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 7:49 am Post subject: |
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| bill wrote: | | Then how come the PhD I sent it to said otherwise. I received a letter from the mathematical association of America for my contributions to math. |
Congratulations. It must have been for something far more complete than what you presented here. Because you still haven't shown why a^4 + b^4 = c^4 + R(a,b). That should be easy to do, if your proof is so trivial and obvious. So why can't you? |
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Kemosabe-TBC Intellectual
Joined: 06 Dec 2008 Posts: 1217 Location: Portugal
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Posted: Tue Dec 22, 2009 8:28 am Post subject: |
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| Truth be told, I've never seen a mathematical proof with a dozen lines. You can't even prove that sqrt(2) is an irrational number with just that number of lines... |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Tue Dec 22, 2009 9:18 am Post subject: |
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Yes Jeffjo it was a little bit more complete. But not much. You see Jeffjo truly gifted mathematicians see what others have overlooked. Sometimes because of all the competition, people like yourself work so hard at studying what others have discovered they fail to look for THEMSELVES.
If you go on the I Google site you will see optical illusions where some people see one picture and others see another. I always see both. Some people are blind to seeing any picture at all. They just see a bunch of lines and cannot make the connections.
Think about the story of Helen Keller. Think about Lenard Euler who when he finally went blind in both eyes stated "Oh now I see everything!" Euler knew he was going blind so he used to practice in the dark writing so when he finally went blind he could continue writing.
By the way Helen Keller had beautiful handwriting herself. Look at Ray Charles and Stevie Wonder. Sometimes it takes a man without sight to show a man with sight what he cannot see. To understand this watch the movie "Circle of Iron". There was also another true story about a women who was continually being raped and beaten by a demon. She went to a university for help and they devised a trap for the demon. They caught him or more correctly the demon let them catch him just to prove he was real. Then the demon broke free which the professors scientists engineers who set the trap thought was impossible.
You see Jeffjo I am trying to help you out of your hypnotic trance you have placed yourself in by studying so hard. You have become unable (not totally) to think for yourself on your own terms.
Imagine yourself in a world where math did not exist yet and you had to discover it and teach it to others. Then imagine yourself in my world where people believe the rules of math were etched in stone and it was heresy to try to write something new. And if you did if you even tried you were beaten and tortured until you recanted and renounced your discovery was wrong and evil and after you did this you were then put to death to save your soul.
Jeffjo I referred to in another post a book entitled An Imaginary Tale by Paul Nahin. It explains why you are wrong about your concept of the sets of numbers (you are also not wrong see the optical illusions I mentioned above). It explains why imaginary was a misnomer. And it explains why i is just as real as any other number. It explains how to find:
Integral from 0 to infinity of sin( x^2) not (sin(x))^2 which was a trivial integral.
Now you know how to take a standard integer derivative. But do you know how to take a fractional derivative. Instead of dny/dnx wher n is an integer dry/drx where r is a rational number.
You see Jeffjo math is all about the imagination and has nothing to do with the real world. The world we can understand. Naturally I am talking about pure math. Then there is applied math which explains natural phenomena and some anomalies. Then there are mathematical anomalies like larger and smaller infinities and larger and smaller zeros, where I had to rewrite what was etched in stone since before this universe began.
Do you play chess Jeffjo. If you did then you would be able to see what you are seeing wrong. I have lost games to rank amateurs but beaten experts at the game. It all depends my mood and frame of mind. I play chess with demons like the one I mentioned above who was beating and raping the woman in the movie I mentioned above. It is played on a board of 12 dimensions. Do you really think I have time to "explain everything" to you. Writing on this post to you Kemo and Rob is my "ludic" activities. The movies by the way do not even come close to the demons I battle. Get the picture Jeffjo. Now people like Rob remind me of the Spanish Inquisition going around shouting BILL IS A HERETIC BELIEVE ME BILL IS A HERETIC DO NOT BELIEVE A WORD HE SAYS
So I laugh at him and make fun of him. You on the other hand Jeffjo are a product of our poor educational system. You are very bright and very erudite. What you have learned; you have learned well; - too well. You have been indoctrinated and inoculated with knowledge but forgot that you have an imagination.
"LIFE JEFFJO IS TO BE IMAGINED NOT LIVED" "IF YOU CANNOT IMAGINE YOUR OWN LIFE IT WILL NEVER BE CREATED" "IT IS THE JOB OF OUR EDUCATORS TO ASSIST OUR CHILDREN IN IMAGINING THAT THEY CAN ALSO CREATE A LIFE FOR THEMSELVES" "A LIFE THEY CAN ASPIRE OTHERS WILL ADMIRE TOO"
Jeffjo do not indoctrinate and inoculate others with the knowledge that you know all too well teach them something new.  _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 10:02 am Post subject: |
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| bill wrote: | | Yes Jeffjo it was a little bit more complete. But not much. |
It is missing a critical step, that you cannot complete.
| Quote: | | You see Jeffjo truly gifted mathematicians see what others have overlooked. |
If by "gifted" you mean "delusional," then I agree. Until you can explain what this missing step is to others who can show it is not true, it exists only in your mind. And that is what a delusion is.
| Quote: | | Sometimes because of all the competition, people like yourself work so hard at studying what others have discovered they fail to look for THEMSELVES. |
The idea of a "proof" is that others shouldn't have to look. The burden is on the prover, to demonstrate everything that is needed.
| Quote: | | Sometimes it takes a man without sight to show a man with sight what he cannot see. |
But if he makes no effort to help others see what he sees, he is just blind. So stop comparing yourself to others who have made such an effort, and instead make that effort yourself.
| Quote: | | You see Jeffjo I am trying to help you out of your hypnotic trance you have placed yourself in by studying so hard. |
And I am trying to help you out of yours, where you think that anything that occurs to you must be true.
| Quote: | | Now you know how to take a standard integer derivative. |
No, I don't. Integers don't have derivatives, functions do.
+++++
Again: why, in your so-called "proof," must a^4 + b^4 = c^4 + R(a,b) ? This is a step you need to make it a proof. It requires no essays on philosophy to supply it, just a simple logical progression. |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Tue Dec 22, 2009 10:07 am Post subject: |
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Jeffjo prove it to yourself if you cannot you will never understand it.
You know nothing about me. You know nothing about what delusional means. How could you I have proven to all psychiatrists that they are delusional.
There are no steps missing just a simple explanation as to why?
So explain why it is a proof to yourself. _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 11:06 am Post subject: |
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| bill wrote: | | Jeffjo prove it to yourself if you cannot you will never understand it. |
I understand it perfectly. I know it doesn't work. And you have not shown otherwise. The reason you haven't, is that you cannot. Even you realize that by now, which is why you refuse to try.
| Quote: | | There are no steps missing just a simple explanation as to why? |
Here it is:
| bill wrote: | Now if n=4 we obtain two different equations:
a^4 + b^4 + R = c^4 R= the sum of the remaining terms after adding.
and
a^4 + b^4 = c^4 this proves it for all even numbers greater than 4.
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Saying "we obtain these equations" proves nothing. You just wrote out what you wanted to see. Show us a valid way you obtained them, and I'll beleive you. It's trivial algebra, after all. While you are at it, show us how...
| bill wrote: | Then I did the same for n=3 and obtained:
a^3 = (d^3 - 3ab^2)/2 = c^3 therefore this proves it for all odd n greater than 2. | ... proves anything at all about a^3+b^3, which does not appear in that equation. |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Tue Dec 22, 2009 11:16 am Post subject: |
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The answer to YOUR QUESTION is STARING YOU RIGHT IN YOUR FACE
Think about what you see Jeffjo do a compare and contrast essay on why there is a difference  _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 11:25 am Post subject: |
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| bill wrote: | | The answer to YOUR QUESTION is STARING YOU RIGHT IN YOUR FACE |
Yes, it is. You do not know how to do it. Otherwise, you could have shown me how long ago. |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Tue Dec 22, 2009 3:26 pm Post subject: |
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Okay Jeffjo
(a+b)^2 = a^2 + b^2 + 2ab = d^2 or ; d^2 - 2ab = c^2 by hypothesis
(a-b)^2 =a^2 + b^2 - 2ab = f^2 or ; f^2 + 2ab = c^2 by hypothesis
Now we add the two and obtain:
2(a^2 + b^2) = d^2 + f^2 = 2c^2 from this we see two things 1) that it is a necessary condition that the R(ab) terms cancel each other out. 2) There exists a^2 + b^2 that equals c^2 it does tell us that such integers exist; it does not tell us what those integers are; it also tells us that there exist an infinite number of them. It also says there must be integers d^2 + f^2 that must equal 2c^2 In other words not just any a^2 + b^2 = c^2 This can easily be seen by plugging in integers. It is a necessary but not a sufficient condition. Now as you will see below this necessary condition of cancellation cannot be met for n greater than 2.
Now since a,b can be any two numbers this exhausts all possibilities by utilizing a+b and a-b. It also tells us that if there exist integers a,b,c for n greater than 2 it is a necessary condition that we must obtain the same outcome. So for n=3 we obtain following the same procedure:
a^3 + 3ab^2 = ( d^3 + f^3 )/2 = c^3 now since the b^3 cancels out this shows that it is not possible. But lets try this:
a^3 + b^3 + 3ab^2 - b^3 now between the sum of any two cubes and a third cube there always exists a difference because of the 3ab^2-b^3; the only time the R(ab) term disappears is when either a or b or both a and b are equal to zero unless of course 3ab^2 - b^3 can equal zero but since a is greater than b the difference is always positive. So for any a^3 + b^3 we have the following difference:
a^3 + b^3 is always different from c^3 . If there existed any a^3 +b^3 = c^3 then there would have to exist an a,b such that 3ab^2 - b^3 is zero. Our hypothesis was false.
Now for n=4
(a+b)^4 = a^4 + b^4 + 4a^3b + 6a^2(b^2) + 4b^3 and
(a-b)^4 = a^4 + b^4 - 4a^3b + 6a^2(b^2) - 4b^3
Adding we obtain a^4 + b^4 + 6a^2b^2 again because c^4 must be different our hypothesis that there exist an a^4 + b^4 = c^4 is wrong because the necessary condition that 6a^2(b^2) = zero can never be met when a, b are greater than zero.
Now I said is there another way:
(a^2 + b^2)^2 and (a^2 - b^2)^2 but then a^2 + b^2 must equal some f^2 or and a^2 - b^2 must equal some g^4 but then this contradicts the above because we have already established that we must eliminate 6a^2(b^2) in order for there to exist an a^4 + b^4 = c^4 and the only difference is the letters.
Now the same holds for all odd and even numbers n greater than 2. Since the necessary condition of cancellation of R(ab) can only be met for n=2 and not for n>2. _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 4:56 pm Post subject: |
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| bill wrote: | Okay Jeffjo
(a+b)^2 = a^2 + b^2 + 2ab = d^2 or ; d^2 - 2ab = c^2 by hypothesis
(a-b)^2 =a^2 + b^2 - 2ab = f^2 or ; f^2 + 2ab = c^2 by hypothesis
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Close: your hypothesis is that a triple (a,b,c) exists, such that a^2 + b^2 = c^2. You defined d=(a+b) and f=(a-b) (skipping over that you want a>b). But this is for n=2. I asked for n=4. But you didn't prove what you think you proved here, so I'll keep following it.
| Quote: | Now we add the two and obtain:
2(a^2 + b^2) = d^2 + f^2 = 2c^2 from this we see two things 1) that it is a necessary condition that the R(ab) terms cancel each other out. |
No, it is consequence. "n=2" is a condition, "terms cancel out" is its consequence.
| Quote: | | 2) There exists a^2 + b^2 that equals c^2 it does tell us that such integers exist; |
It tells us no such thing. You assumed that.
| Quote: | | it does not tell us what those integers are; it also tells us that there exist an infinite number of them. |
There is no "infinite number," because you haven't proven any exist. All you "proved" is that if you can find integers that satisfy a^2+b^2=c^2, then a^2+b^2=c^2. As I said before, this is not earth-shattering. In fact, there isn't the slightest trace of a tremor.
| Quote: | | It also says there must be integers d^2 + f^2 that must equal 2c^2 |
So? You defined d and f to be the sum & difference of a and b. Are you now surprised they turned out to be integers? Or that you can rearrange the hypothesized equation to include them? This proves nothing.
| Quote: | | In other words not just any a^2 + b^2 = c^2. This can easily be seen by plugging in integers. |
Right - only pythagorean triples. So? Do you realize that also means "not just any d=a+b and f=a-b?
| Quote: | | It is a necessary but not a sufficient condition. |
What, exactly, do you think that means? Because you aren't using the terms correctly.
| Quote: | Now as you will see below this necessary condition of cancellation cannot be met for n greater than 2.
Now since a,b can be any two numbers ... |
No, they can't. You "hypothesized" they were integers that made up a pythagorean triple. Remember? "(a+b)^2 = ... = c^2 by hypothesis."
| Quote: | | ... this exhausts all possibilities by utilizing a+b and a-b. It also tells us that if there exist integers a,b,c for n greater than 2 it is a necessary condition that we must obtain the same outcome. |
(1) You mean that it is a consequence that we obtain that outcome,
(2) You didn't make it clear what outcome you meant,
(3) If that outcome is "d and f can be any integers," you are wrong, because (a,b,c) are limited to pythagorean triples, and
(4) No, it does not mean that the same outcome follows for larger n. You have to demonstrate that for each n individually. This is one of your missing steps.
| Quote: | So for n=3 we obtain following the same procedure:
a^3 + 3ab^2 = ( d^3 + f^3 )/2 = c^3 |
Again, you hypothesized that there exist a triple (a,b,c) such that a^3+b^3=c^3, and defined d=a+b and f=a-b.
But nothing you did has shown that (d^3+f^3)/2 = c^3. You copied the left-side of the "n=2" equation, and changed the "^2"s to "^3"s. It isn't true BECAUSE THERE SHOULD BE AN R TERM IN THERE SOMEWHERE. And you don't use this relationship for anything, anyway.
| Quote: | | now since the b^3 cancels out this shows that it is not possible. |
Shows that what is not possible? Why? What has it to do with a^3+b^3=c^3, or (d^3+f^3)/2=c^3?
| Quote: | But lets try this:
a^3 + b^3 + 3ab^2 - b^3 now between the sum of any two cubes and a third cube there always exists a difference because of the 3ab^2-b^3; |
No, not "any two cubes." You defined d and f relative to a and b. They can't be "any" values, the can only be specific values. There are cubes not represented by your variables.
| Quote: | the only time the R(ab) term disappears is when either a or b or both a and b are equal to zero unless of course 3ab^2 - b^3 can equal zero but since a is greater than b the difference is always positive. So for any a^3 + b^3 we have the following difference:
a^3 + b^3 is always different from c^3. |
No, you didn't show that. You showed that a^3 + b^3 was always different from (d^3+f^3)/2. There is no c^3 in what you have actually shown.
| Quote: | | If there existed any a^3 +b^3 = c^3 then there would have to exist an a,b such that 3ab^2 - b^3 is zero. Our hypothesis was false. |
You have not shown this.
| Quote: | Now for n=4
(a+b)^4 = a^4 + b^4 + 4a^3b + 6a^2(b^2) + 4b^3 and
(a-b)^4 = a^4 + b^4 - 4a^3b + 6a^2(b^2) - 4b^3
Adding we obtain a^4 + b^4 + 6a^2b^2 again because c^4 must be different |
Why must c^4 be different? You only showed that a^4 + b^4 + R(a,b) = (d^4+f^4)/2. There is no "= c^4" at the end of that.
| Quote: | | Now I said is there another way: |
Just as flawed.
+++++
Here is all that you have shown, and I've expanded it a bit: if you start with any two numbers such that a>b; and if you define d=a+b, f=a-b, then:- If n is even, a^n + b^n + R(n,a,b) = (d^n + f^n)/2
- If n is odd, a^n + R(n,a,b) = (d^n + f^n)/2
where R(n,a,b)=0 if n=1 or n=2, and R(n,a,b)>0 if n>2
You have related this to a c^n in only one case, that of n=2. Since R(2,a,b)=0, you showed that (d^n+f^n)/2=c^n. BUT ONLY FOR n=2, and ONLY BECAUSE YOU ASSUMED a^n+b^n=c^n |
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bill Intellectual
Joined: 22 Apr 2006 Posts: 1204
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Posted: Tue Dec 22, 2009 5:43 pm Post subject: |
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Jeffjo you just changed the name which means nothing. Then it is a necessary consequence in order for there to exist abc. You are mincing words and splitting hares.
It is necessary for this consequence to occur/happen/exist in order for such and such to be true.
It is necessary for this condition to occur/happen/exist in order for such and such to be true.
Anyone can change words of equivalent meanings Jeffjo. And then argue from there that there is a difference.
It is a necessary consequence/condition that the "terms cancel out". You are trying to play word games.
It tells us our hypothesis is true. But you have to deny this in order to say you are right and I am wrong. You assume your assumptions are right. My equation proves that the hypothesis of the existence of such numbers exist.
Jeffjo you argue ass backwards.
f and d are two numbers that are created by two other numbers a and b. According to the way you argue you could easily say a and b cannot be added or subtracted.
When you do a proof Jeffjo you start at a hypothesis which I did. Then I constructed two different equations that when added proved the hypothesis correct. You can argue and mince words until you are blue in the face Jeffjo. But mincing words and using semantics does not prove me wrong. It only proves you want to be right and the only person who is right can be you. You Jeffjo are not a mathematician you are a cynic.
My equations say such integers must exist Jeffjo not if they exist. But you deny this Jeffjo. I explain to you what the equations mean and the best you can do is deny what I say. This means either one of two things either you are breaking my balls (I do not mind I broke your balls) or you actually do not understand what a mathematical proof is unless you read it out of a math book.
So I will assume you are just breaking my balls. _________________ love creation machine |
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JeffJo Intellectual
Joined: 10 Mar 2009 Posts: 1019
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Posted: Tue Dec 22, 2009 6:10 pm Post subject: |
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On "necessary condition" | bill wrote: | | Jeffjo you just changed the name which means nothing. Then it is a necessary consequence in order for there to exist abc. You are mincing words and splitting hares. |
Half rabbits aside, it shows that you have no idea what I meant in other threads, when I used the term. I understood what you wanted the first time you used it (btw, all consequences are necessary. That's why they are called consequences).
| Quote: | | It is necessary for this condition to occur/happen/exist in order for such and such to be true. |
But that isn't how you used it. You used it for the "such and such" that you wanted to be true.
| Quote: | | Anyone can change words of equivalent meanings Jeffjo. And then argue from there that there is a difference. |
Sure. It's your forte. I like to keep to the established meanings, since it helps communication work.
| Quote: | | My equation proves that the hypothesis of the existence of such numbers exist. |
No, your n=2 equatiion was your hypothesis. You used it to derive itself. That proves nothing.
| Quote: | | f and d are two numbers that are created by two other numbers a and b. According to the way you argue you could easily say a and b cannot be added or subtracted. |
Certainly they can be added and subtracted. But they can't have "any value," they can only be a+b and a-b.
| Quote: | | When you do a proof Jeffjo you start at a hypothesis which I did. Then I constructed two different equations that when added proved the hypothesis correct. |
No, you did not. You just re-created your hypothesis.
| Quote: | | My equations say such integers must exist Jeffjo not if they exist. |
Not only didn't you prove them, they don't show any such thing.
+++++
Again, why do the parts in red follow:
a^3 + 3ab^2 = ( d^3 + f^3 )/2 = c^3
a^4 + b^4 + 6a^2b^2 = c^4 |
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