The Foundations of a Non-Naive Mathematics

[Hurkyl]

If you're adding, as axioms, that |{}| = 0 and |{__}| = 1, then we can now prove:

If 0 and 1 are different, then {} and {__} are different. (Assuming that | | is supposed to be a logical function)

You still can't prove any of the things I said you couldn't prove, though.

 

[Lama]

Again, axioms are not proven

|{}|=0 , |{__}|=1 (The 1 continuum)

Please read http://www.geocities.com/complementarytheory/No-Naive-Math.pdf (please start from page 10 until the end of my article, if you wish to understand my work).

 

[Hurkyl]

Yes, but things may only be proven from axioms.

(Incidentally, any axiom proves itself)

 

[Lama]

Do you want to understand my work or not?

If yes then please read http://www.geocities.com/complementarytheory/No-Naive-Math.pdf (please start from page 10 until the end of my article).

 

[Hurkyl]

http://www.geocities.com/complement...-Naive-Math.pdf doesn't work.

Does it have more axioms than the ones you listed in #260?

 

[Sporg]

terrabyte has been banned. He used to call himself ram1024, ram2048, ram4096, etc. We have banned this person three times already, yet he still does not seem to understand that he is not welcome here, and nor are his pointless threads.

If any of you see activity that you suspect is due to the same individual, please let the staff know so we can deal with it.

- Warren

Warren, i get the feeling that you don't like me...

for the record, i wasn't banned three times i was banned once for all three accounts. for "spamming" which i wasn't. but that's neither here nor there.

 

[Lama]

doesn't work.

My first response to "doesn't work" was:
(If you cannot understand what are the unreachable limits of any information system (including the Langauge of Mathematics) and how I use the reachable information forms, which exist between these unreachable limits, to create Math that is based on an Included-Middle reasoning, then dear Hurkyl I cannot help you.)

Then I realized that it is technically doesn't work, so sorry about my first response and here it is again the link of my work: http://www.geocities.com/complementarytheory/No-Naive-Math.pdf (please start from page 10 until the end of my article).


Please read a post of mine to Matt, to understand more https://www.physicsforums.com/showpost.php?p=270261&postcount=255

Thank you.

 

[Lama]

Here is again a list of my axioms, which are related to R:

A definition for a point:
A singleton set p that can be defined only by tautology ('='), where p has no internal parts.

A definition for an interval (segment):
A singleton set s that can be defined by tautology ('=') and ('<' or '>'), where s has no internal parts.


The axiom of independency:
p and s cannot be defined by each other.

The axiom of complementarity:
p and s are simultaneously preventing/defining their middle domain (please look at http://www.geocities.com/complementarytheory/CompLogic.pdf to understand the Included-Middle reasoning).

The axiom of minimal structure:
Any number which is not based on |{}|, is at least p_AND_s, where p_AND_s is at least Multiset_AND_Set.

The axiom of duality(*):
Any number is both some unique element of the collection of minimal structures, and a scale factor (which is determined by |{}| or s) of the entire collection.

The axiom of completeness:
A collection is complete if an only if both lowest and highest bounds are included in it and it has a finite quantity of scale levels.

The Axiom of the unreachable weak limit:
No input can be found by {} which stands for Emptiness.

The Axiom of the unreachable strong limit:
No input can be found by {__} which stands for Fullness.

The Axiom of potentiality:
p {.} is a potential Emptiness {}, where s {._.} is a potential Fullness {__}.

The Axiom of phase transition:
a) There is no Urelement between {} and {.}.
b) There is no Urelement between {.} and {._.}.
c) There is no Urelement between {._.} and {__}.

Urelement (http://mathworld.wolfram.com/Urelement.html).


The axiom of abstract/representation relations:
There must be a deep and precise connection between our abstract ideas and the ways that we choose to represent them.


(*) The Axiom of Duality is the deep basis of +,-,*,/ arithmetical operations.

Tautology means x is itself or x=x.

Singleton set is http://mathworld.wolfram.com/SingletonSet.html .

Multiset is http://mathworld.wolfram.com/Multiset.html .

Set is http://mathworld.wolfram.com/Set.html .

(By the way the diagrams in my papers are also proofs without words http://mathworld.wolfram.com/ProofwithoutWords.html )



The Axiom of the paradigm-shift:

Within any consistent system, there is at least one well-defined set, which its content cannot be well-defined within the framework of the current system.



Let us stop here to get your remarks.

 

[arildno]

"A definition for a point:
A singleton p that can be defined only by tautology ('='), where p has no internal parts."

1. What is a singleton?
2. What is "="?
3. What is an "internal part"?
4. What is an external part?

 

[Lama]

1. What is a singleton?
2. What is "="?

1. Singleton set http://mathworld.wolfram.com/SingletonSet.html
2. Tautology (x is itself or x=x).

3. What is an "no internal parts"?
4. What is an external part?

3. Non divisible or Urelement (http://mathworld.wolfram.com/Urelement.html).
4. I did not use these words.

(By the way the diagrams in my papers are also proofs without words http://mathworld.wolfram.com/ProofwithoutWords.html )

 

[Erck]

A point with no internal parts does not exist.

 

[Lama]

You missed the point.

I said "no internal parts".

Which means, it is non-divisible.

 

[hello3719]

A definition for a point:
A singleton set p that can be defined only by tautology ('='), where p has no internal parts.

A definition for an interval (segment):
A singleton set s that can be defined by tautology ('=') or '<' or '>', where s has no internal parts.

A number is consider as a point in your system right ?

If yes, then by the 1st definition it would follow that there can only exist one number,because in our system, numbers are constructed using previous numbers (ex. 1 + 1 = 2) Unless i misunderstood the internal parts thing.

 

[Lama]

A number is consider as a point in your system right ?

A number in my system is |{}| or p_AND_s , where p_AND_s is at least Multiset_AND_Set.

 

[hello3719]

A number in my system is |{}| or p_AND_s

what is |{}| ?

 

[Lama]

The cardinal of {}.

 

[matt grime]

But, Doron, the only people to agree with anything you've said are also cranks (though moshek is borderline), so let me have my fun. Remember you're the one who asked me to come here and comment on your work. Tough if you don't like it.

 

[Lama]

Matt, there is a time (after more then a year) when you have to realize that you have no ability to give any useful comment about my work, because you demonstrate time after time that its most basic principles are beyond your basic intuitions that you have about the language of Mathematics and its reasoning.

I can show you the most beautiful things in the world, but if you are blind to them, then it is a waste of time for both of us.

As I said before (https://www.physicsforums.com/showpost.php?p=270261&postcount=255), in my opinion your school of thought is based on the shadow of the intuitions of my school of thought.

If you insist and give comments to things that you cannot see (understand) then this is your problem.

 

[Lama]

Let us think about Mandelbrot set http://aleph0.clarku.edu/~djoyce/julia/julia.html .
The set itself is the black areas, where no information can be found.

This black area is the invariant or the constant side of Mandelbrot set, but the other side of it is its border area, where the interesting information is created when Mandelbrot set goes to infinity.

No one of these sides can be ignored if we want to understand what is a Mandelbrot set.

The same approach has to be used if we want to understand what is R collection.

Any R member is a unique (invariant and constant) element in the collection, but on the same time each constant is a scale factor of the entire R collection.

It means that the entire R collection exists between two opposite states (minus is the mirror -not the oppisie- of plus side).

In one state, when 0 is the scale factor, no R member except 0 can be found.

On the other state No R member can be found when we reach oo (as clearly can be shown here: http://www.geocities.com/complementarytheory/RiemannsLimits.pdf ).

Furthermore, because of this duality of any R member, we get a system which is both absolute (when a single scale is examined) and relative (where the same place of the real line is examined simultaneously on several different scales).

Another example:

Pi = the relations between the perimeter and the diameter of a circle.

Pi is invariant in any arbitrary given scale, but when several scale levels are simultaneously compared, we can clearly see that each circle has a different curvature.

If our system is a circle, then if we want to understand what is a circle, then both its invariant and its variant properties cannot be ignored.

(We also have to be aware to the fact the no circle can be found when Diameter or Perimeter = 0, or Diameter or Perimeter = oo.

In short, our basic approach is to find the gateways between opposite properties, and the best way to do it, is by an including-middle logical reasoning (http://www.geocities.com/complementarytheory/CompLogic.pdf).

 

[Hurkyl]

You claim that standard mathematics is a "shadow" of your system.

This suggests that you can take any concept or any proof in your system, and simply look at its shadow to get something in standard mathematics.

To state this again, you should be able to provide a standard mathematical description of some concept by taking your concept and looking at its shadow.

You should be able to provide proof that would be acceptable in standard mathematics simply by taking your proofs and looknig at the shadow.


You keep claiming that standard mathematics is merely a shadow of your system, but you never demonstrate any understanding of the shadow.

 

[Lama]

You keep claiming that standard mathematics is merely a shadow of your system, but you never demonstrate any understanding of the shadow.

If someone developing a x,y,z system, he first must understand the a x,y system.

If you understand my work (and you did not demonstrate this even once), then you can clearly see that I understand the foundations of the standard x,y system.

On the contrary all we need is, for example, to read your reply in https://www.physicsforums.com/showthread.php?p=273568#post273568 in order to understand that you have no sense of symmetry to simple mathematical ideas.

Please demonstrate some fundamental mathematical idea, which can clearly show that I do not understand (again, not disagree with, but do not understand) its standard interpretation.

 

[moshek]

Matt , I ask now your explantion to that :

"But, Doron, the only people to agree with anything you've said are also cranks (though moshek is borderline), so let me have my fun. Remember you're the one who asked me to come here and comment on your work. Tough if you don't like it."


Moshek

 

[matt grime]

YOu ask for comments, Doron, and because they aren't what you want to hear you dismiss them. You know nothing of mathematics as you repeatedly demonstrate, and I will keep pointing out where you make gross errors in your representations of what mathematics is, or does. You make lots of mistakes and say things that are out right lies abot mathematics; I will not stand for that.

 

[Lama]

You are a seek person Matt, and I am going to call your university to tell them that, if you continue to bother me.

 

[quantumdude]

This is a Forum, Lama. You have no right to tell anyone not to respond to your posts, and you certainly have no right to threaten reprisals against anyone who does.

 

[Hurkyl]

I'll start with binary logic.


You've had trouble understanding quantification.

"For all q, P(q)"
"There exists z such that P(z)"

(Where, in both cases, P is some logical proposition, and I've specifically used letters other than x for the dummy variables to indicate that x is not special)


You've had trouble understanding proof by contradiction.

From "If P then false"
We conclude "not P"

 

[Lama]

This is a Forum, Lama. You have no right to tell anyone not to respond to your posts, and you certainly have no right to threaten reprisals against anyone who does.

Do you allow a parson like Matt to write what ever he likes, including to hurt another persons that are posting in my thread (https://www.physicsforums.com/showpost.php?p=274454&postcount=292), without any limits to his vulgarity?

Is there any tool in this forum where I can block persons like Matt?

 

[Lama]

I'll start with binary logic.

1) My reasoning is not binary logic, because binary logic is a trivial logical reasoning, when you look at it from the point of view of an included-middle logical reasoning, as you clearly can see in http://www.geocities.com/complementarytheory/CompLogic.pdf.

And I developed my included-middle logical reasoning system, after I understood the triviality of the binary logic.

2) The triviality of a proof by contradiction and the trivial use of a universal quantification as something that can be related to a collection of infinitely many elements, are clearly demonstrated here: http://www.geocities.com/complementarytheory/Anyx.pdf

 

[quantumdude]

Do you allow a parson like Matt to write what ever he likes, including to hurt another persons that are posting in my thread (https://www.physicsforums.com/showpost.php?p=274454&postcount=292), without any limits to his vulgarity?

It looks like you have a different definition of "vulgar" than I do, because I don't consider calling someone a crank to fall in that category.

Is there any tool in this forum where I can block persons like Matt?

Yes, you can use the "Ignore" feature. It will take Matt's posts right off your screen. In fact you can use that feature to make all voices of disagreement evaporate from your screen. Wouldn't that be wonderful?

 

[Lama]

Tom Mattson,

It looks like you have a different definition of "vulgar" than I do, because I don't consider calling someone a crank to fall in that category.

1) I do not care when Matt call me a crank (sometimes you can find 'crakpot' or 'idiot' in his "rich" vocabulary), but when he add other persons as cranks just because they understand my work, then for me he went too far.

2) Matt did not write any meaningful comments on my work, because he did not show any ability to understand it.

When time passes, he becomes more and more aggressive and instead of write about my work, he writes about me, which is irrelevant.

Please see by yourself his basic tune in this thread.

On the contrary you can see persons that can understand my work, for example: https://www.physicsforums.com/showpost.php?p=266203&postcount=76 and also have a high-quality ability to communicate and explain themselves.

you can use the "Ignore" feature

In this forum I do not have any abilities except of open a new thread or add and edit my posts only in "theory development", i even have no ability to get or send private messages, or to see public profiles or change my profile.

In fact you can use that feature to make all voices of disagreement evaporate from your screen

This is a cynic and unnecessary response from a person that his job is to be a super mentor of a public forum.

Can you give us the reason why you clearly take Matt's side?