Deeper than primes

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zooterkin said:
ETA: What do you get if if multiply 0.333... by 3?
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0.999...


zooterkin said:
If you're trying to say that there is not an infinite number of points on any line, then you're clearly wrong, unless you would care to identify some place on the line where there is no point, or two points between which there is not another.
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≠ of k-dimA ≠ k-dimB ≠ k-dimB ≠ ... is exactly some domain on the n-dim where no k-dim exists.
 
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realpaladin said:
The infinite is often (or perhaps always?) an approximation of the large finite.

Continuous structures are often cleaner, more symmetric, and richer than their discrete
counterparts (for example, a planar grid has a much smaller degree of symmetry than the whole euclidean plane).

It is a natural and powerful method to study discrete structures by "embedding" them in the continuous world.

A classical example is the use of generating functions (with a continuous variable) to analyze the structure of a sequence.

But there are many other important examples. Methods from algebraic topology have been used to prove purely combinatorial statements.

It is quite easy to formulate the most important combinatorial optimization problems as linear programs with integrality conditions, and it is quite easy to solve these, if we disregard the integrality conditions; the game is to find ways to write up these linear programs in such a way that disregarding integrality conditions is justified.
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So <snip> is all you get ( http://www.internationalskeptics.com/forums/showpost.php?p=4909717&postcount=5240 ).

As a result you are using Sraw Man ( http://en.wikipedia.org/wiki/Straw_man ).
 
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zooterkin said:
and what do you get if you divide 1 by 3?
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1/3, where 0.333...[base 10] < 1/3


zooterkin said:
So you are saying there are two points on a line between which there is not another?
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I say that the whole idea of more than a one point on a line, 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.

Please read very carefully http://www.internationalskeptics.com/forums/showpost.php?p=4909686&postcount=5236 .

EDIT:

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 (the atomic state > k-dim).
 
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realpaladin said:
No, I am just writing something and you are not responding to it.

A straw-man is if I use a weaker version of your statements to defeat them.

This time, I have not referred to your statements so I can not be using a straw man.

I would like you to respond, that is all.
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You are talking about the usefulness of the current paradigm.

I am talking about the vary begging of a new paradigm.

Find the differences.
 
doronshadmi said:
1/3,
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Yes, that's 1 divided by three...
where 0.333...[base 10] < 1/3
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By how much is 0.333... less than 1/3?

What value do you get if you actually perform the division manually?



I say that the whole idea of more than a one point on a line, does not hold if ≠ is avoided.
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What exactly do you mean by that? You can only have one point on a line?

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.

Please read very carefully http://www.internationalskeptics.com/forums/showpost.php?p=4909686&postcount=5236 .

EDIT:

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 (the atomic state > k-dim).
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Sorry, I don't speak gibberish.
 
zooterkin said:
Sorry, I don't speak gibberish.
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:)

And the reason Doron does not answer me because he knows quite well that OM is just doing the opposite of maintaining the integrality of continuous mathematics.

OM needs fundamentally discreet building blocks, he states it time and again.

So, how does your precious One Mathematics and Organic Mathematics meet again?

Hautain behaviour will only get you nowhere on this forum.
 
doronshadmi said:
You are talking about the usefulness of the current paradigm.

I am talking about the vary begging of a new paradigm.

Find the differences.
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Well, I am now going to report myself, but it served my purpose.

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.

This leads me to conclude two things;

- You just like to link to stuff you think nobody is going to read anyway.
- You like namesdropping.
 
realpaladin said:
Well, I am now going to report myself, but it served my purpose.

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.

This leads me to conclude two things;

- You just like to link to stuff you think nobody is going to read anyway.
- You like namesdropping.
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Quoting X is not necessarily Getting X.

realpaladin said:
You did not recognize it and started arguing against it.
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On the contrary, I took the continuous and the discrete, and rigorously showed the exact results of the linkage of these fundamental concepts.

It is a paradigm-shift of these fundamental concepts.
 
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doronshadmi said:
On the contrary, I took the continuous and the discrete, and rigorously showed the exact results of the linkage of these fundamental concepts.

It is a paradigm-shift of these fundamental concepts.
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You did nothing of the sort! Read back the posts! No weaseling here Doron.
 
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