Deeper than primes

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realpaladin said:
My 'statement' was a quote from the linked 'One Mathematics' http://www.cs.elte.hu/~lovasz/berlin.pdf

It was that single call for unification of mathematics by Mr. Lovasz.

You did not recognize it and started arguing against it.
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doronshadmi said:
Quoting X is not necessarily Getting X.
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What does it mean when you read X, don't recognise it as a quote from something you yourself posted as supporting your ideas, then start arguing against it?

Just when I start to think you've exhausted all the possible ways to be wrong ... you pull a classic like this!

Are you watching, MosheKlein?
 
zooterkin said:
One over infinity. In other words, 1 divided by infinity. (Not infinity plus one.)
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1/infinity has nothing to to with the structural fact that no amount of k-dim elements can fully cover a 1-dim element.

Furthermore, we can't break structure 1 into more than one piece and still claim that these pieces are the same as the 1 structure, before we broke it into pieces.

So as you see, exactly because of this structural difference no amount of k-dims can fully cover n-dim.

Furthermore, no amount of more than 1 n-dims, is the same as 1 n-dim, if Structure is considered.

For example:

___ is not the same as _ + _ + _ , if Structure is considered.
 
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doronshadmi said:
1/infinity has nothing to to with the structural fact that no amount of k-dim elements can fully cover a 1-dim element.

Furthermore, we can't break structure 1 into more than one piece and still claim that these pieces are the same as the 1 structure, before we broke it into pieces.

So as you see, exactly because of this structural difference no amount of k-dims can fully cover n-dim.
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So, where are the gaps? Where on a 1-dim line do you not find a 0-dim point?



To continue the other part of the discussion, if you divide 1 by 3, then multiply by 3, what is your answer?
 
zooterkin said:
So, where are the gaps? Where on a 1-dim line do you not find a 0-dim point?
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Exctly where ≠ (which is a projection of n-dim between any pair of k-dims on it) is used as a differentiator between more than one k-dim on it.


zooterkin said:
To continue the other part of the discussion, if you divide 1 by 3, then multiply by 3, what is your answer?
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Furthermore, no amount of more than 1 n-dims, is the same as 1 n-dim, if Structure is considered.

For example:

___ is not the same as _ + _ + _ , if Structure is considered.
 
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Let us put it this way:

We say that the whole idea of more than a one k-dim on n-dim, does not hold if ≠ is avoided.

It is clear that ≠ is an invariant fact between any arbitrary pair of k-dim elements on n-dim element, even if ∞ scale factor is used.

After all also at ∞ scale factor level we still have k-dimA ≠ k-dimB ≠ k-dimC ... , which is more than a single k-dim element on a n-dim element.

In other words, the important thing here is the structural difference between the actual state of "many" (whether it is finitely many or infinitely many) and the actual state of the one (n-dim atomic state > many k-dim state, where the id of each k-dim has no significance).



Some claims:



"I may try reproduce how I understand your text:
k-dim elements with respect to n-dim element can't be taken otherwise as redundancies of uncertainessnesses or something like with algebra of these things yet to be developed. Thus, for n-dimensionality whatever k-dimensional is in one exemplar essentially, saying with some philosophical air. Let be so. Is this organic mathematics? Then mathematics is already organic if taken in this sense."


My comments are:

By the current paradigm n-dim = many k-dim state.

This is not the case by the Organic paradigm where n-dim state > many k-dim state.

The amount of k-dims on n-dim has nothing to do with their ids.

≠ is a projection of n-dim as a differentiator between more than one k-dim on it, no matter what id each k-dim has.

In that case k-dimA ≠ k-dimB ≠ k-dimC ... is reduced to the amount aspect, that can be written as k-dim ≠ k-dim ≠ k-dim ... .

For example: k-dim ≠ k-dim ≠ k-dim has cardinality 3, whether the k-dims are distinguishable or not.

By extending the cardinality to ∞ , we still find ≠ as a projection of n-dim, which is used as a differentiator between more than one k-dim on it.

At the moment that the Organic paradigm is understood, then, for example:

0.999…[base 10] < 1 exactly by 0.000…1 , where the "…1" of "0.000…1" is equivalent to ≠ as a projection of n-dim, between non-finite amount of

0.9(≠) + 0.09(≠) + 0.009(≠) + … k-dims and 1 n-dim (no amount of many k-dims, whether they are distinct or not, can fully cover n-dim).



As we all know 0.999…[based 10] is currently considered as a numeral of number 1.



This is not the case by the Organic paradigm, where 0.999…[based 10] is considered as a non-local number and 1 is considered as local number of "0.999…[base 10] < 1" expression..
 
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doronshadmi said:
This is not the case by the Organic paradigm, where 0.999…[based 10] is considered as a non-local number and 1 is considered as local number of "0.999…[base 10] < 1" expression..
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If you divide 1 by 3, then multiply by 3, what is your answer?
 
Now:

0.999… / 1 = 0.999… / 1 < 1 by 0.000…1

exactly as, for example, 0.999 / 1 = 0.999 / 1 < 1 by 0.001


1 / 0.999… = 1.000...1
 
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doronshadmi said:
0-dim:3 or 0-dim/3 is exactly the same building-block that can be on one and only one location along a 1-dim building-block.

1-dim:3 or 1-dim/3 is exactly the same building-block that can be in more than a one location along a 1-dim building-block.

So the operation has no significance as long as we deal with atoms, whether they are local or not.

At the moment that you understand that "…1" of the expression "0.000…1" is a 1-dim atom, then and only then you are able to understand
"0.999…[base 10] < 1" expression.

Again, 1-dim/∞ ≠ 0-dim exactly because:

n=1 to ∞
k= n-1 to ∞

Any n-dim is non-local with respect to any amount of k-dim elements because: given n-dim element, there are infinitely many k-dim elements on it such that k-dimA ≠ k-dimB ≠ k-dimC …, where ≠ is an example of n-dim domain, which is not covered by any k-dim element. If some claims against this assertion then he has to avoid ≠. But then there is at most one and only one k-dim elements on the n-dim element. By carefully investigate the dimensions' example it is discovered that ≠ is equivalent to n-dim, and it is clearly shown that Non-locality and Locality are different mathematical spaces that are associated but not defined by or made of each other, similarly to two axioms. This example can be used without loss of generality in many mathematical branches, and this generalization actually provides a non-trivial way for "One Mathematics" [1], which we call "The Organic Unity of The Mathematical Science" [2].


[1] L. Lovasz: One Mathematics http://www.cs.elte.hu/~lovasz/berlin.pdf .

[2] Moshe Klein, Doron Shadmi: Organic Mathematics, International Journal of Pure and
Applied Mathematics, volume 49 No. 3 2008, 329-340
http://www.geocities.com/complementarytheory/IJPAM-OM.pdf
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Well if “ …the operation has no significance as long as we deal with atoms…” then that leaves your ‘atomic’ notions rather limited when it comes to distinct operations.

Once again your notions do not seem to take into consideration the actual aspects involved. If we consider a circle with a radius R equal to 1 and then consider a specific one third portion of that circle as any arc of any radius R that subtends 120 degrees, one might consider that a “building-block” of any complete circle of R radius, such as the R = 1 circle. If on the other hand we consider a 1:3 scaled down version of that R = 1 circle thus having a radius of R = 1/3 then it is still a complete circle and not a “building-block” of any complete circle of R radius, since it is itself a complete circle of R radius. Scaling always maintains the aspect ratios and completeness of what is scaled. While division specifically does not maintain the completeness of what is divided nor does it have to maintain the aspect ratios of what is divided. Again completely different and distinct concepts and operations for very specific reasons and applications. You seem to apply your notions strictly linearly and do not seem to consider either circular or curvature considerations or even multi-dimensional considerations as simple as just a flat plane.
 
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