The Foundations of a Non-Naive Mathematics

[Lama]

Dear zeronem,

Thank you for this information.

 

[Lama]

Please define " one dimensional path of a base 10 fractal". There is a big problem here with definitions.

There is no big problem here if you understand this model:

http://www.geocities.com/complementarytheory/9999.pdf

I'll be glad to get your opinion, thank you.

 

[zeronem]

By the way, what is your Mathematical Background Lama? How far have you gotten in your math classes at school?

The answer to these questions will let us know exactly who we are talking to.

 

[moshek]

Zeronem:

If you talk like this,
it is better for you
not to know
who you are talking with.

Moshek

 

[matt grime]

"I am a mutation"

well, you said it, Doron.

Muddler, as to the proof that 0.99.. =1 in the reals (base ten expansion), it would appear that Doron is once more using his own definitions to conclude something about ours.

Something that should warn you he's off on one is that he doesn't ever use any of the parts of the definition of the real numbers to prove anything.

Here is a simple proof:

consider the sequences 1,1,1,1,1... and 0.9, 0.99, 0.999, now the "symbol" 0.99999... means the limit of the second. Now, it follows that these are clearly both cauchy sequences, and the difference between them is a cauchy sequence tending to zero, hence, that the sequences represent the same real number. (Which follows from the characterization of the reals as equivalence classes of cauchy sequences of rational numbers).

In fact we have all seen his characterzation of duality and scale factor and such. Now, all of the things he says about the reals are valid about the rationals and hence do not in anyway characterize reals uniquely.

 

[terrabyte]

.999... ≠ 1 is one of my favorite topics

so many exceedingly smart people get it wrong. it is quite clear that when functioning under limits you cannot expect your tried and true methods to yield correct results.

.999... is NOT 1. it's simple and logical

 

[matt grime]

In the reals, in base 10 representations, 0.999... and 1 are equivalent, and equal in this sense. they may be taken to represent different cauchy sequences, but they are unequivocally the same real number, Terrabyte. Please, offer a reason, mathematically sound, as to why they are not equal.

 

[Hurkyl]

you and other "well-educated" colleagues of the academic system, prefer to protect the dogmatic core of your community, instead of let it be developed by an open dialog.

As long as you continue to believe this, you will have shut out a great store of knowledge and innovation.

You will do your best to shut me down and I will do my best to survive and flourish.

As long as you reject criticism, you will not flourish. It is just as important, if not more so, to understand one's mistakes than to understand one's successes.



Do you remember long ago when I was working with you? I stated that I felt it important to understand how your ideas related to mathematics, and eventually decided that, among anything I could try to do, helping you understand that relation would be the most beneficial to you. I still think that is true.

 

[Lama]

Now, all of the things he says about the reals are valid about the rationals and hence do not in anyway characterize reals uniquely.

Please read again http://www.geocities.com/complementarytheory/No-Naive-Math.pdf

You can find there:

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

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

3) A number is both p_AND_s

4) A general representation of an interval (segment) is {._.}.

5) A general representation of a point is {.}.

6) Only {._.} can be affected by a scale factor.


Both Q and R members are effected by using one of them as a scale factor over the entire Real-Line.

The difference between Q and R members is still the inability to define an R member (irrational) by a ratio between at least two integers.

But this is not the new case here.

The new thing is that any given number is now both absolute and relative element, because it is defined by ({},{_}):={x|{} <-- x(={.}) AND x(={._.})--> {_}}.

 

[Lama]

By the way, what is your Mathematical Background Lama? How far have you gotten in your math classes at school?

The answer to these questions will let us know exactly who we are talking to.

I am an autodidact that dealing (with a lot of love and patience) with the Langauge of Mathematics for more then 20.

 

[Lama]

As long as you reject criticism...

On the contrary, I seek for criticism (otherwise I would not be hear) and you are maybe one of the best.

But the sad thing is that I used your criticism to develop my system, and you react as if nothing has been changed during the years.

To be more specific: please criticize https://www.physicsforums.com/showpost.php?p=267089&postcount=101

Thank you.

 

[kaiser soze]

You receive criticism only when you agree with it. If you really want to learn, you need to be able to accept criticism even if you do not initially agree; this because you acknowlegde that whom ever criticizes you knows more than you do in the acclaimed subject...

Kaiser.

 

[Lama]

You receive criticism only when you agree with it...

Please show me an example of how a person can receive criticism, and on the same time he does not agree with it.

In short, 'receive' and 'agree' are synonyms in this case, isn't it?

 

[kaiser soze]

I'll try an analogy: when a parent says to his little child "do not speak to strangers", the child should accept this "criticism", even if the reason is unclear at that moment. When this child grows up, it will become clear to him why this "criticism" was given.

Kaiser.

 

[Lama]

I'll try an analogy: when a parent says to his little child "do not speak to strangers", the child should accept this "criticism", even if the reason is unclear at that moment. When this child grows up, it will become clear to him why this "criticism" was given.

Your analogy does not hold in this case, because we are talking about fundamental things which are the heart bits that give life to the language of Mathematics.

In this most simple level we do not need sophisticated methods but very sensitive intuition/reason gentle interactions, which become our self-evident building-blocks that are used as the milestones of our research.

What I have found is, that instead of developing this gift of self research that exists in most of the young students, the academic system does its best to force its methods on the minds of the students, because there is no time and no money to develop the unique internal skills of each student.

As a result the student is forced to be under the doctrine of some external method which he must agree with it in every step along the "learning" process.

After couple of years under this forcing external race-like method, most of the students are not able to use anymore their natural skills of self learning, and most of them become no more then good technicians of the academic system.

I have found that a lot of doctors and professors of Mathematics simply lost any ability to understand simple things.

My work is on these simple things, and I developed my skills to work and create in this simple level, for more then 20 years.

No external reasons like money or academic title where my motivations and no forcing external race-like methods washed my natural ability to understand simple things.

 

[kaiser soze]

Mathematics was developed and taught long before academic institutions existed, yet its fundamental concepts and foundationds are still valid.

Kaiser.

 

[Lama]

Mathematics was developed and taught long before academic institutions existed.

Yes, it developed by people who where not forced by external methods or exteral reasons or lack of time.

yet its fundamental concepts and foundationds are still valid.

Not all of them.

 

[kaiser soze]

The least I can offer you, is to accept and learn from others, who may have more knowledge from you in a given area - that is if you wish to interact with them.

Kaiser.

 

[Lama]

Dear kaiser soze,

Please show some detailed example, which cearly show why my work failes because I am not listening to persons that have more knowledge in this given area.

 

[kaiser soze]

you refuse to accept the simple fact that the LIMIT of the sequence 0.9, 9.99, 0.999, ... is 1.

Kaiser.

 

[Lama]

Don't you see the simple fact, which can clearly understood by https://www.physicsforums.com/showpost.php?p=267089&postcount=101 that 1 is not the limit of your sequence?

 

[kaiser soze]

I rest my case.

 

[terrabyte]

In the reals, in base 10 representations, 0.999... and 1 are equivalent, and equal in this sense. they may be taken to represent different cauchy sequences, but they are unequivocally the same real number, Terrabyte. Please, offer a reason, mathematically sound, as to why they are not equal.

you're essentially limiting the structure of your numerical system by this "entity" we call infinity. now, infinity is a useful term, we use it frequently to extend expressions out to incredible precision, but since the term itself is not closed, there lacks a decided "conclusion" for formulas utilizing infinity. thus any formulas that use infinity are relegated to being approximations, albeit really damn good ones.

the limit of a sequence is something that is NEVER reached. hence defined as such 1 IS the limit of .9+.09+.009...

but from that statement above it's logically sound that since it is NEVER reached, the sequence can NEVER be equal to 1.

the flaw is in the system, whether we choose to fix it or ignore it is the question...

 

[sparkster]

Wow...I came over here hoping to find some info on the recent experiment that supposedly disproves the Copenhagen interpretation of QM. Imagine my surprise when I see my friend Dorian (known as Lama here) posting this stuff here. And I was even quoted! I am indeed honored.

If anyone is interested, my dialogues with him are here, http://www.iidb.org/vbb/showthread.php?t=89321

 

[Lama]

Welcome my dear ex-xian,

I invite you to continue our dialog here or in your forum.

An information of this recent experiment you can find here:

http://drauh.typepad.com/blog/2004/04/

http://www.kathryncramer.com/wblog/archives/000530.html

Since Quantum elements are both wave and particle, no one of these properties can completely disappear, so I do not see any new point in this recent experiment.

 

[Hurkyl]

the academic system does its best to force its methods on the minds of the students

Do you see the irony in that you are trying to force your ideas on others?

 

[Lama]

Do you see the irony in that you are trying to force your ideas on others?

Am I an academic institute that gets money for my knowledge and forces people to show that they got it, by using an industry of examinations that if they do not pass them they will not get their diploma?

Can you please show how I force you to agree with me?

By the way, I am still waiting to you at https://www.physicsforums.com/showpost.php?p=267696&postcount=116

 

[sparkster]

Welcome my dear ex-xian,

I invite you to continue our dialog here or in your forum.

An information of this recent experiment you can find here:

http://drauh.typepad.com/blog/2004/04/

http://www.kathryncramer.com/wblog/archives/000530.html

Since Quantum elements are both wave and particle, no one of these properties can completely disappear, so I do not see any new point in this recent experiment.

Then you don't follow what's happening. Apparantly, this is the first time that light has been both a wave and a particle and not either/or.

Anyway, it hasn't been published, it hasn't been repeated. It's very preliminary, yet you insist on making dogmatic, authoritative statements. This is indicitive of your way of rejecting established science out of hand in order to favor your own bizarre theories.

With all due respect, I'll wait for real scientists who have spent decades doing this to decide rather than taking your opinion.

About your theories. I'm getting ready for graduate school next month, which I'm spending all my free time doing actual mathematics. I've responded to your posts again and again. You ignore what I write (the construction of the reals w/o using points--which invalidates your theory), take my words and use your own defintion (the "well-defined" bit), or you totally misunderstand what I write and put your own odd spin on it (my example of a delta-epsilon proof).

 

[sparkster]

Yes, it developed by people who where not forced by external methods or exteral reasons or lack of time.

Not all of them.

You've never even come close to showing this.

 

[sparkster]

you're essentially limiting the structure of your numerical system by this "entity" we call infinity. now, infinity is a useful term, we use it frequently to extend expressions out to incredible precision, but since the term itself is not closed, there lacks a decided "conclusion" for formulas utilizing infinity. thus any formulas that use infinity are relegated to being approximations, albeit really damn good ones.

the limit of a sequence is something that is NEVER reached. hence defined as such 1 IS the limit of .9+.09+.009...

but from that statement above it's logically sound that since it is NEVER reached, the sequence can NEVER be equal to 1.

the flaw is in the system, whether we choose to fix it or ignore it is the question...

There's no flaw in the system. When I was taking my calculus classes, my teachers always made a point to emphasize that when we say a sequence or series equals a number, we really mean that the sequence has limit of that number. Saying "equals" is just shorthand. That's not to say, however, that 0.99... is not equal to 1.

Here's a really simple way of showing that 0.99... = 1 that doesn't involve limits.

Clearly, 1/3 = 0.333...
So 3(1/3) = 3(0.333...)
Thus 1 = 0.999...

 

[Lama]

This is not the first time that both wave and particle properties of a quantum element, simultaneously appearing in a physical experiment.

When both stils are opened and we check the photons after they passé both of them, we can change gradually the wave picture to a particle picture, and vice versa.

 

[sparkster]

This is not the first time that both wave and particle properties of a quantum element, simultaneously appearing in a physical experiment.

When both stils are opened and we check the photons after they passé both of them, we can change gradually the wave picture to a particle picture, and vice versa.

Thanks, I think everyone knows this. And this is totally not what I'm talking about. You should actually read up on this topic before you try to discuss it anymore.

 

[Lama]

ex-xian,

I'll be glad to get your opinion on https://www.physicsforums.com/showpost.php?p=267089&postcount=101

 

[sparkster]

ex-xian,

I'll be glad to get your opinion on https://www.physicsforums.com/showpost.php?p=267089&postcount=101

My opinion is that it's juvevile and wrong.

Assume that .99.. < 1. Then 1/3(.999) < 1/3 (1), and .33... < 1/3. A contradiction, therefore .999 >/= 1. By a similar argument, .99... is not > 1. Therefore .99.. = 1.

Please, instead of citing old posts or referncing your own papers, actually address what I wrote if you want to prove me wrong.

 

[Lama]

Please give your detailed explanation why do you think it is wrong?