The Martian and the Earthman - and the limit concept

[Organic]

I think that your claim to have shown that the Collatz conjecture was undecidable in ZFC because it was equivalent to the axiom of infinity amply demonstrates that you are ignorant of fundamental mathematical concepts.

An axiom is an arbitrarily true within its own Mathematical universe; therefore cannot be proven within its own Mathematical universe.

Therefore we have to be very careful when we define some axiomatic system.

Any proof which is equivalence to an axiom, has the above state, no more no less ( my 3n+1 proof can be found here: http://www.geocities.com/complementarytheory/3n1proof.pdf )

(ie saying set ! XOR set 2).

Please give the address where you have found (set ! XOR set 2).

Apparently saying that 0.999... is not one

It can be found here: http://www.geocities.com/complementarytheory/99999.pdf

refusing to accept the definition of the real numbers as the completion of the rationals in the eucliden norm

It can be found here: http://www.geocities.com/complementarytheory/NewDiagonalView.pdf

Everyone makes mistakes.

I totally agree with you.



Also it will be interesting to see how professional mathematicians have the ability to reexamine the set concept through an open dialog as I suggesting here:

https://www.physicsforums.com/showthread.php?t=18972

 

[matt grime]

But if nothing can be proven true then nothing can be proven true. You claimed that within ZFC it was undecidable, therefore the negation must be consistent with the axioms of ZFC, as the negation would imply the axiom of infinity isn't true (and exioms are true by definition) then you were wrong to claim it was undecidable.

Every mathematical statement has implicit and explicit assumptions that tell you under what circumstances things are true. As long as we don't forget that we are fine.

For instance that 0.999.. =1 is true is implicitly assuming we are talking about base 10 expansions of real numbers, where the real numbers are the completion wrt the euclidean norm. In your words, to mimic kaiser soze, no more no less. We make no more claims that than.

 

[Organic]

But if nothing can be proven true then nothing can be proven true. You claimed that within ZFC it was undecidable, therefore the negation must be consistent with the axioms of ZFC, as the negation would imply the axiom of infinity isn't true (and exioms are true by definition) then you were wrong to claim it was undecidable.

Again, this the 0 XOR 1 Boolean Logic point of view, no more no less.

Please read this: http://www.geocities.com/complementarytheory/CuRe.pdf

For instance that 0.999.. =1 is true is implicitly assuming we are talking about base 10 expansions of real numbers, where the real numbers are the completion wrt the euclidean norm. In your words, to mimic kaiser soze, no more no less. We make no more claims that than.

In your world 0.999...=1 and you move to the next problem.

In my world [0.000..., x) not= 0 and infinitely many information forms can be found and researched, for example: http://www.geocities.com/complementarytheory/epiphi.pdf

 

[moshek]

Kaiser soze Hi:

Please tell me what is the deferent
between mathematical true to any belief ?

Thank you
Moshek

 

[kaiser soze]

Moshek,

how do you define a "mathematical true"?

kaiser.

 

[matt grime]

"Please tell me what is the deferent
between mathematical true to any belief ?"

can someone please translate that so it makes the slightest sense?

 

[Organic]

Maybe instead of belief we can talk on hidden assumptions which can stand in the basic of our reasoning when we define some logical system, for example, let us take again the delta-epsilon proof by contradiction:


If |a-b| = d < all e > 0 then d = 0.

Proof:

Let us say that d > 0

1. d < all e > 0
2. d > 0

Since d < all e > 0 and d > 0 then d<d that cannot be true, so 1. and 2. cannot both be true.

Therefore, it is true that "If 1, then not 2 --> d = 0", QED.

The hidden assumptions:

This proof holds only if there is a complete collection of infinitely many r members > 0 and 0 is a positive number.

But if there is no such a thing like a complete collection of infinitely many r members > 0 and 0 is not a positive number (because the logical system has no excluded middle) then e>d>0 proportions are a simple fact that holds in any arbitrary given scale.

 

[matt grime]

Where do we need that 0 is positive? Your personal misconceptions about what the word 'all' signifies is not important.,

 

[pig]

Ok Organic,

Let's do this your way.

0<d<e = true

Since d/2<e, e can't be d/2.

Since e can't be d/2, and d/2>0, there is a number > 0 that e cannot be.

Therefore, it isn't true that "for all e>0, d<e" - we found at least one number > 0 we are not allowed to select as e in order to uphold your "0<d<e" law :)

Of course, if you were serious about the possibility of "A AND NOT A" being true, then it is impossible to prove not only this, but anything to you.

Instead of "0<d<e" you can say that "for all e>0, d<e" is true and must hold, but then we get that "0<d<e" isn't true.

And if you call BOTH of those statements facts which must hold, then that is just like saying that "a<3" and "a>5" must both hold - it leads us to A AND NOT A.

 

[Organic]

Pig,

Therefore, it isn't true that "for all e>0, d<e" - we found at least one number > 0 we are not allowed to select as e in order to uphold your "0<d<e" law :)

You steel forcing the logic of 1 XOR 0 "true" on the idea of the open collection of infinitely many elements, which are ordered in infinitely many scales.

Thouogh this point of view this proportion "e>d>0" can be found in any given arbitrary scale (please think about an endless zoom-in scale of a fractal), and it has no connection to 1 AND 0 logic.

More then that, you look on A and not_A from 1 XOR 0 point of view.

Try to look at A and not_A from Complementary Logic point of view:
http://www.geocities.com/complementarytheory/BFC.pdf

Do you think you can do that?

Where do we need that 0 is positive? Your personal misconceptions about what the word 'all' signifies is not important.,

If 0 is not a positive number then it does not belong to r>0 collection and you cannot state that If
|a-b| = d < all e > 0 then d = 0, because 0 is not in the scope of r>0.

My non-standard point of view that a incomplete collection of infinitely many
r>0 over infinietly many incomplete levels of scales, gives the existence to "e>d>0" proportion.

 

[matt grime]

"If 0 is not a positive number then it does not belong to r>0 collection and you cannot state that If
|a-b| = d < all e > 0 then d = 0, because 0 is not in the scope of r>0."

That makes no sense, unsurprisingly. Of course I can do the 'comaprison'.

 

[Organic]

Dear Matt,

By your reasoning (which is based on the excluded middle) what is the positive real number which is smaller then all r>0?

Be aware that if 0 is not a positive number, then you are not in the excluded middle logical system.

 

[matt grime]

no, d is a number greater than or equal to zero that is less than all strictly positive numbers, there's no problem here.

 

[Organic]

no, d is a number greater than or equal to zero that is less than all strictly positive numbers, there's no problem here.

And what is the reason that d can be >= 0?

Can -r <= 0?


By the way I agree with you that 0 as a positive number, is not a "must have" condition to find that an incomplete collection of infinitely many r>0 over infinietly many incomplete levels of scales, gives the basis to the existence of "e>d>0" proportion.

 

[pig]

Organic, yes, the proof is based on the assumption that a statement is either true or false, never both. If you don't agree with that, nothing can be proven, since anything you prove true can still also be false, and anything proven false can still be true.

 

[matt grime]

the d we are referring to is the absolute value of some real number, so it is not negative, what are you getting at now?

 

[Organic]

the proof is based on the assumption that a statement is either true or false

and this way of thinking is limited to 0_redundancy_AND_0_uncertainty information form, which is a one and only one proper sub_system of infinitely many information forms that can be ordered and explored by Math Language.

The paradigm shift is based on the idea that there are infinitely many ordered information forms where any combination of them can be a basis to another information model that can be explored and used to develop new point of views on Math fundamental concepts like axiom, number, set, limit, operation, logic, function, infinity and so on.

Shortly speaking, I am talking about infinitely many combinations of infinitely many information forms upon infinitely many scales that can be ordered by infinitely many symmetry and information's clarity degrees.

Do you think that it will be a wise thing to simply ignoring all this and stick only in one and only one information form of 0_redundancy_AND_0_uncertainty?

 

[matt grime]

As you've not managed to show one single use of your new point of view, or explain the meaning of almost any of the terms you use, I think we can safely ignore your view.

 

[Organic]

Complementary Logic universe ( http://www.geocities.com/complementarytheory/BFC.pdf ) is an ordered logical forms that existing between a_XOR_b and a_AND_b.

For example:

Let XOR be #

Let AND be &

Let a,b,c,d stands for uniqueness, therefore logical forms of 4-valued logic is:

              Uncertainty
  <-Redundancy->^
    d  d  d  d  |
    #  #  #  #  |
    c  c  c  c  |
    #  #  #  #  |
    b  b  b  b  |
    #  #  #  #  |
   {a, a, a, a} V
    .  .  .  .
    |  |  |  |
    |  |  |  |
    |  |  |  | <--(First 4-valued logical form)
    |  |  |  |
    |  |  |  |
    |&_|&_|&_|_
    |
    ={x,x,x,x}


   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  | <--(Last 4-valued logical form)
    |#____|  |      
    |        |
    |#_______|
    |
    ={{{{x},x},x},x}

[b]
============>>>

                Uncertainty
  <-Redundancy->^
    d  d  d  d  |          d  d             d  d
    #  #  #  #  |          #  #             #  #        
    c  c  c  c  |          c  c             c  c
    #  #  #  #  |          #  #             #  #   
    b  b  b  b  |    b  b  b  b             b  b       b  b  b  b
    #  #  #  #  |    #  #  #  #             #  #       #  #  #  #   
   {a, a, a, a} V   {a, a, a, a}     {a, b, a, a}     {a, a, a, a}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |  |  |  |       |&_|_ |  |       |#_|  |  |       |&_|_ |&_|_
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |  |  |  |       |     |  |       |     |  |       |     |
    |&_|&_|&_|_      |&____|&_|_      |&____|&_|_      |&____|____
    |                |                |                |
    {x,x,x,x}        {x,x},x,x}       {{{x},x},x,x}    {{x,x},{x,x}}     
 
                                      c  c  c
                                      #  #  #      
          b  b                        b  b  b          b  b
          #  #                        #  #  #          #  #         
   {a, b, a, a}     {a, b, a, b}     {a, a, a, d}     {a, a, c, d}
    .  .  .  .       .  .  .  .       .  .  .  .       .  .  .  .
    |  |  |  |       |  |  |  |       |  |  |  |       |  |  |  |
    |#_|  |&_|_      |#_|  |#_|       |  |  |  |       |&_|_ |  |
    |     |          |     |          |  |  |  |       |     |  |
    |     |          |     |          |&_|&_|_ |       |#____|  |
    |     |          |     |          |        |       |        |
    |&____|____      |&____|____      |#_______|       |#_______|
    |                |                |                |
    {{{x},x},{x,x}} {{{x},x},{{x},x}} {{x,x,x},x}      {{{x,x},x},x} 

   {a, b, c, d}
    .  .  .  .
    |  |  |  |
    |#_|  |  |
    |     |  |  
    |#____|  |      
    |        |
    |#_______|
    |    
    {{{{x},x},x},x}
[/b]

A 2-valued logic is:

    b   b 
    #   #    
    a   a     
    .   .   
    |   |   
    |&__|_   
    | 
    
    [B]a   b     
    .   .   
    |   |  <--- (Standard Math logical system fundamental building-block) 
    |#__|   
    |[/B]

Do you start to understand the triviality of Standard Math logical system,
when each n has several ordered logical forms between a_AND_b and a_XOR_b?

Please look again at these ordered information forms http://www.geocities.com/complementarytheory/ETtable.pdf , but now instead of numbers please look at them as infinitely many unique logical forms that are "waiting" to be explored and used by us.

I hope that you start to understand the flexibility of any language, when you examine it from the level of the information concept.

 

[moshek]

kaiser.
thank you for asking me :

"how do you define a "mathematical true"?

so :


"Mathematical true is a unification of the local property of an object
to it Global property by the two size of the Klein Bottle "



Moshek

p.s :

Since i am not talking about Euclidian mathematic please read before:

www.physicsforums.com/showthread.php?t=17243

 

[kaiser soze]

Moshek,

I do not understand your definition, but anyhow, according to Webster's Revised Unabridged Dictionary, © 1996 :

Belief:

\Be*lief"\, n. [OE. bileafe, bileve; cf. AS. gele['a]fa. See Believe.] 1. Assent to a proposition or affirmation, or the acceptance of a fact, opinion, or assertion as real or true, without immediate personal knowledge; reliance upon word or testimony; partial or full assurance without positive knowledge or absolute certainty; persuasion; conviction; confidence; as, belief of a witness; the belief of our senses.


So in any case, you can see that whatever your definition of a "mathematical truth" is, as long as it stays within the domains of sciense can not be compared with a belief.

Kaiser.

 

[moshek]

Matt,

Why do you even bother arguing with Organic? Can't you see that his actions are not
Motivated by curiosity or pure interest, instead they are motivated by beliefs. You can
Not argue with beliefs. Arguing with Organic, is like arguing with an orthodox person about the existence of god. It is Organic's BELIEF that mathematicians are wrong, and for that matter, that he KNOWS mathematics and practicing it. It is his belief that the he has found a "new type" of infinity, and that this is the "right one". Arguing with Organic is a just a waste of time, since he does not really want to learn or do anything practical with his ideas.

Kaizer

Thank you for sharing with me what Webster wrote about believe.

My definition to mathematics like Organic is defiantly not in way science see mathematics. but science after Einstein need a new mathematics when the observer is part of the universe, and not the modeling attitude of Newton.
the only way to do that shift is by new definition to the concept of a number like Organic have share with you !

Best
Moshek

 

[matt grime]

No, Moshek, Mathematics was remarkably unmoved by Einstein. What people choose to do with the practical implications doesn't alter the mathematics. Newtons equations are still consistent, that they don't work all the time has nothing to do with mathematics. You and Organic both need to learn more of the maths that is out there before you start making these laughable claims about the suitability of your language/dialogue/theory. In particular it might do for you to adhere to some of the basic ettiquette of generalization: you have not redefined the natural numbers, you have defined a new object (in some loose sense) that might conceivably have some relation to the natural numbers.