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Deeper than primes

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doronshadmi said:
( http://en.wikipedia.org/wiki/Dedekind_cut )

r is some rational number such that A={x:x<r} and B={x:x≥r}.

An irrational number z must be > all A members AND < all B members, in other words > and < are involved here such that < is actually the non-locality between z and all A members or the non-locality between z and all B members.
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Dedekind Cuts has no reliance on Doronetics. Your attempt to force in your irrelevant concepts does nothing but emphasis your lack of understanding of Dedekind Cuts.
 
jsfisher said:
Dedekind Cuts has no reliance on Doronetics.
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Dedekind Cuts has no reliance on anything. It is idiotic exactly as Lebesgue measure 0 has nothing to do with Cantor set simply because there is no homeomorphism between 0-dimensional and 1-dimensional spaces.

Your "death by entropy" closed box reasoning is not going to survive.
 
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doronshadmi said:
You continue to evade the answer (for example) in http://www.internationalskeptics.com/forums/showpost.php?p=7338074&postcount=15847.
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Hey, you invented the notation. If you can't tell us what you meant by 0.000...1, don't expect me to tell you what you meant.

However, if you wish to insist that 0.000...1 is exactly equal to 1 - 0.999... and rely on that as your definition, then your contrived notation is just unnecessary and silly. The rest of us just use 0 to represent that number.
 
doronshadmi said:
epix, do you agree that your measured curve is 1-dim\0-dims co-existence?

Please answer only by yes or no.
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No, coz the curve is not "measured." Only straight lines can be measured, coz they represent unique (the shortest) distance between two locations on some manifold. The length of curves must be arrived at with a method, which depends on the nature of the curve.

You bemoaned another ghost of yours that traditional math invents problems that don't exist. That curve I posted does exist and its length is unknown altogether with the way it was drawn (no function). So why don't you show the traditional mathematicians how OM solves problems that do exist. In other words, show there is a coexistence between OM and a practical application.
 
epix said:
That curve I posted does exist and its length is unknown altogether with the way it was drawn (no function).
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I see that you are unaware of the fact that the function of your drawn curve has measurable results only under at least 1-dim\0-dims co-existence.
 
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jsfisher said:
It what way does it behave differently from 0?

So far, all you have done (out of your own ignorance) is simply proclaim it is different from 0. Bare assertions do not equal proof.
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jsfisher, there is no homeomorphism between 1-dimensional expression like 0.000...1[base 10] and any given 0-dimensional expression.

Dedekind Cuts has no reliance on anything. It is idiotic exactly as Lebesgue measure 0 has nothing to do with Cantor set simply because there is no homeomorphism between 0-dimensional and 1-dimensional spaces.

You simply unable to get the irreducibility of 1-dimensional element to 0-dimensional element, exactly because the power of the continuum is at least 1-dimensional element, and no amount of 0-dimensional elements along it has this power.

The irreducibility of 1-dimensional element to 0-dimensional element is an axiom (no proof is needed).

Your reasoning can't get http://www.internationalskeptics.com/forums/showpost.php?p=7343628&postcount=15859 .
 
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doronshadmi said:
jsfisher, there is no homeomorphism between 1-dimensional expression like 0.000...1[base 10] and any given 0-dimensional expression.
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You claimed it was > 0. All you need do is show how it behaves differently from 0. Why is this a problem for you?
 
doronshadmi said:
Dedekind Cuts has no reliance on anything. It is idiotic exactly as Lebesgue measure 0 has nothing to do with Cantor set simply because there is no homeomorphism between 0-dimensional and 1-dimensional spaces.
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In other words, L cannot relate to C, coz interdimensional H doesn't exist. But where is the idea that it does? There are things out there that one can't overlook.
The automorphisms of the binary tree are its hyperbolic rotations, and are given by the modular group. Thus, the Cantor set is a homogeneous space in the sense that for any two points x and y in the Cantor set C, there exists a homeomorphism with h(x) = y. These homeomorphisms can be expressed explicitly, as Mobius transformations.

The Hausdorff dimension of the Cantor set is equal to ln(2)/ln(3) = log3(2).
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doronshadmi said:
I see that you are unaware of the fact that the function of your drawn curve has measurable results only under at least 1-dim\0-dims co-existence.
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I said that the function that drew the curve is unknown -- I wouldn't offend advanced OM methods with something that can be done via the traditional L = a∫b√([f'(x)]2 + 1) dx.

jcurve.png


Just set B - A = 1 doron and come up with the best approximation there is in the whole Universe and beyond and beyond still . . .
 
jsfisher said:
You claimed it was > 0. All you need do is show how it behaves differently from 0. Why is this a problem for you?
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What exactly prevents from you to understand that 0.000...1[base 10] is some particular example of the truth about the irreducibility of 1-dimensional element to 0-dimensional element?
 
doronshadmi said:
What exactly prevents from you to understand that 0.000...1[base 10] is some particular example of the truth about the irreducibility of 1-dimensional element to 0-dimensional element?
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I can highly recommend Alex's Adventures in Numberland by Alex Bellos. It's a very entertaining and informative book, and it also addresses many of the things you find confusing.
 
doronshadmi said:
What exactly prevents from you to understand that 0.000...1[base 10] is ...<irrelevant attempt to evade original question>...
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So, you can provide nothing to distinguish it from 0 (other than your bare assertion).
 
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jsfisher said:
So, you can provide nothing to distinguish it from 0 (other than your bare assertion).
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EDIT:

Once again, what exactly prevents from you to understand that 0.000...1[base 10] is some particular example of the the self evident truth about the irreducibility of 1-dimensional element to 0-dimensional element?

Why can't you grasp that without non-locality\locality co-existence there is no multiplicity?

The simplest example of this self evident truth is 0-dimasional elements (localities), which are connected by 1-dimensional element (non-locality) (see the second illustration below).

Be aware of the fact that 0-dimesional or 1-dimesional elements are not limited only to metric space, but they are actually generalized to any framework which enables the existence of multiplicity, such that their inability to be transformed to each other guarantees the existence of multiplicity under co-existence.

For example: .__.____._.__. is an illustration of 5 localities and 4 non-localities, or .__.____._.__. is an illustration of 5 localities and 1 non-locality, under co-existence.

Furthermore, the power of the continuum is expressed as the non-locality under non-locality\locality co-existence, which is a self evident truth that your local-only reasoning can't comprehend.
 
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