The Foundations of a Non-Naive Mathematics

[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?

 

[quantumdude]

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.

I don't think Matt does call Moshek a crank because he understands your work. I think he calls him a crank for independent reasons.

https://www.physicsforums.com/showthread.php?t=23442

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

Funny, every single real mathematician at every message board to which you post, says the same about you.

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.

I see both his tune, and your tune. You do the same thing to him that he does to you. But even so, you cannot expect him to accede to your request that he not post in your threads anymore. To put a finer point on it, they aren't even "your" threads.

And you certainly have no place to call his university over it.

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.

Well then I guess you'll have to ignore Matt the old fashioned way.

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?

Oh, brother.

I don't clearly take Matt's side. If I did, then I'd be deleting your ad hominem arguments against him, while leaving his in place. But as it is, I pretty much leave the two of you alone. I only stepped in here because you threatened to interfere with his personal life.

 

[Lama]

Tom Mattson,

Thank you for your clear answer.

 

[sparkster]

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.

How about a limit. You've tried to do a proof with one, but you just embarass yourself.

 

[Lama]

Why, because I clearly show (http://www.geocities.com/complementarytheory/Anyx.pdf) that nothing is approaching to some constant, if our collection is infinitely many elements in infinitely many different scales?

Please see my axioms if you want to understand my system:
https://www.physicsforums.com/showpost.php?p=272134&postcount=278

Also please read this:
https://www.physicsforums.com/showpost.php?p=273614&postcount=289

 

[Hurkyl]

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

If it was so trivial, you should be able to understand it, né? You should be able to, for instance, give a proof by contradiction that any mathematician would accept as valid... no matter what your opinions on the subject are.

 

[Lama]

In an included-middle logical reasoning there is no contradiction (http://www.geocities.com/complementarytheory/CompLogic.pdf).

 

[kaiser soze]

if your system contains the "standard" system, then you should have contradictions.

Kaiser.

 

[sparkster]

In an included-middle logical reasoning there is no contradiction (http://www.geocities.com/complementarytheory/CompLogic.pdf).

Then why have you tried to a proof, that involved a limit, by contradiction?

Besides, this isn't the point. You claimed to have a solid understanding of "standard" mathematics. I challenge you to present a proof, any proof, that demonstrates your so-called understanding.

 

[Lama]

if your system contains the "standard" system, then you should have contradictions.

Some analogy:

Let us say that to get a glue we need a combinations of matirial A and matirial B.

A has its unique properties, which is not a property of a glue.

B has its unique properties, which is not a property of a glue.

When we combine between A and B we get property C, which is the glue, and then we are using the Glue for our perpos.

My logical system is C.

And A and B are Boolean Logic and Fuzzy Logic, which their own properties are not used, when we get C state.

For better understanding please look at http://www.geocities.com/complementarytheory/CompLogic.pdf pages 1-3.

Thank you.

 

[Hurkyl]

If boolean logic was a part of your system, then you should be able to demonstrate an understanding of boolean logic.

 

[Lama]

Then why have you tried to a proof, that involved a limit, by contradiction?

I used a proof by contradiction only to show the standard Math point of view on the limit concept and how it is using a universal quantification on a collection of infinitely many elements, which are existing in infinitely many different scale level, which is something that I disagree with.

And I clearly demonstrated why a universal quantification cannot be related to this kind of a collection(http://www.geocities.com/complementarytheory/Anyx.pdf)

I challenge you to present a proof, any proof that demonstrates your so-called understanding.

No problem, please read this:
http://www.geocities.com/complementarytheory/PZstar.pdf

 

[sparkster]

Okay, for any lurkers, here's the sequence of events. Lama/Dorian/Organic/Math Crank states that his "system" subsumes "standard" mathematics. Okay, fair enough. It is pointed out that if this is the case, he should be extremely knowledgeable and proficient in the "standard mathematics." Lama asks for any topic at all so he can demonstrate his knowlege.

To quote,

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.

Upon being asked to demonstrates his knowledge about ideas, he then proceeds to explain why he disagrees with the issues, something he specifically stated wasn't his intention in the above quoted post.

There is some back and forth, some of us pointing out his inconsitency, to which he replies with this gobbeldygook.

Some analogy:

Let us say that to get a glue we need a combinations of matirial A and matirial B.

A has its unique properties, which is not a property of a glue.

B has its unique properties, which is not a property of a glue.

When we combine between A and B we get property C, which is the glue, and then we are using the Glue for our perpos.

My logical system is C.

And A and B are Boolean Logic and Fuzzy Logic, which their own properties are not used, when we get C state.

For better understanding please look at http://www.geocities.com/complementarytheory/CompLogic.pdf pages 1-3.

Thank you.

What the hell does this have to do with proving that you actually know math? Explain a limit (w/o copying and pasting or posting links), do a proof of a limit by defintion, do an actual proof by contradiction (w/o copying and pasting or posting links), do anything.

You keep avoiding the issue. We all know that you disagree with it all--nobody cares. You challenged us to come up with something about which we thought you were ignorant and you were going to prove us wrong. So far, you've failed at proving anything (but you should be used to that by now).

 

[CrankFan]

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

Funny, every single real mathematician at every message board to which you post, says the same about you.

Well, obviously Tom: No real mathematician has the acuity to comprehend the brilliance of Lama's work.

Let this serve as a notice to all you real mathematicians. Lama has dropped hints indicating that the conflict which emerges as a result of his struggle against the Bodyguards-of-math_TM to expound on his important ... uhm ... hallucinations, on this virtually unknown web forum may well end in a cataclysmic event whereby mathematicians fall from grace and a are replaced by a golden age, ruled by... uhm... incompetent kooks like Lama.

Anyway, since he's obviously onto the Bodyguards-of-math_TM, at the very least I suggest that you guys no longer do the secret handshake in public.

 

[sparkster]

[

I used a proof by contradiction only to show the standard Math point of view on the limit concept and how it is using a universal quantification on a collection of infinitely many elements, which are existing in infinitely many different scale level, which is something that I disagree with.

And I clearly demonstrated why a universal quantification cannot be related to this kind of a collection(http://www.geocities.com/complementarytheory/Anyx.pdf)

Nothing you've ever written has ever been clear and nothing you've tried to do has demonstrated anything.

No problem, please read this:
http://www.geocities.com/complementarytheory/PZstar.pdf

Big surprise. You repost something that you've already posted under a different name (I'm assuming that you included the corrections that everyone gave you in the other thread?)


ETA: Can you define your symbols? I've them all mean different things in abstract algebra, analysis, and set theory, and it's not at all clear what you're doing.

It appears that you're trying to show that a set cannot have the same cardinality of it's power set, but some of your symbolism is confusing.

 

[Lama]

Dear ex-xian,

What exactly is your problem, can't you understand my axiomatic system?
https://www.physicsforums.com/showpost.php?p=272134&postcount=278

Cant you understand my original point of view here:
http://www.geocities.com/complementarytheory/PZstar.pdf

Is this the reason that you so aggressive and jumpy?

To get a better picture of this paper please look at:
http://www.geocities.com/complementarytheory/Identity.pdf including all of its links, thank you.