Deeper than primes

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jsfisher said:
Please, just stop, Doron. The failures are completely your own, not those of anyone else. You are not helping your cause by continually exposing your inabilities.
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Please, just start, jsfisher. The context-depended-only reasoning is your "death by entropy" closed box.You are not helping your cause by continually exposing your inabilities to get out of it.
 
epix said:
And that concludes the non-rigorous proof that the number of all points, which satisfy the definition of the real number and which are positioned alongside a 1-dim object, is independent of the magnitude of such an object.
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Nonsense.

Traditional mathematics asserts that a collection of |R| 0-dimensional elements can be equivalent to an element that has length > 0.

epix said:
Care to demonstrate the essence of the "power of the continuum?" How does OM figure the length of this object?
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The length of an element > 0 is determined by locality\non-locality co-existence. No collection 0-dimensional elements can do it without their co-existence with 1-dimensional elements, and only the 1-dimensional elements have the power of the continuum under this co-existence.
 
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doronshadmi said:
Please, just start, jsfisher. The context-depended-only reasoning is your "death by entropy" closed box.You are not helping your cause by continually exposing your inabilities to get out of it.
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If only you had something you could present to prove you case....

Something, that is, other than the misunderstanding of simple concepts, circular reasoning, contradictory statements, and accusations that it really is everyone else who have the failings you so clearly demonstrate.

Got anything like that?
 
doronshadmi said:
Nonsense.

Traditional mathematics asserts that a collection of |R| 0-dimensional elements can be equivalent to an element that has length > 0.
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Why don't you include a quote from some source that makes the basis of your claim?
The length of an element > 0 is determined by locality\non-locality co-existence. No collection 0-dimensional elements can do it without their co-existence with 1-dimensional elements, and only the 1-dimensional elements have the power of the continuum under this co-existence.
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So go ahead and describe the way OM handles the task as opposed to the way traditional math does it. Here is another, easier object you can demonstrate the OM method on.

The-J-Curve_blanksm.jpg


Suppose the curve is randomly drawn and you need to know its length.
 
epix said:
Why don't you include a quote from some source that makes the basis of your claim?
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Any closed interval [a, b] of real numbers is Lebesgue measurable, and its Lebesgue measure is the length b−a. The open interval (a, b) has the same measure, since the difference between the two sets consists only of the end points a and b and has measure zero.
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( http://en.wikipedia.org/wiki/Lebesgue_measure )
|b−a| > 0 even if [a,b] is (according to traditional math) no more than a set of 0-dimensional elements.

epix said:
So go ahead and describe the way OM handles the task as opposed to the way traditional math does it.
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Very simple. OM asserts that |b−a| > 0 is possible only by, at least, 1-dimensional\0-dimensional co-existence, where 1-dimensional element is the minimal non-local expression and 0-dimensional element is the minimal local expression of this co-existence.

Actually, without non-locality\locality co-existence, no Lebesgue measurable can be done, including 0 measurement, which is defined only w.r.t an element that its measurement > 0, exactly as an element that its measurement > 0 is defined only w.r.t an element that its measurement = 0.

It means that non-locality\locality are mutual AND independent w.r.t each other (their different ids are defined and saved under mutuality, such that being mutual AND independent means that the measured is not totally mutual AND not totally independent).

Being not totally mutual AND not totally independent is exactly the organic realm.

So according OM, the real line is at least the co-existence of 1-dimensional element AND 0-dimensional elements along it, such that no amount of 0-dimensional elements has the power of the continuum, which is at least length > 0 (a property that at least 1-dimensional element has under 1-dimensional\0-dimensional co-existence).

epix said:
Suppose the curve is randomly drawn and you need to know its length.
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It can be done only under 1-dimensional\0-dimensional co-existence.

---------------------

This co-existence does not exist by context-dependent-only reasoning.

For example, Cantor set elements are irreducible into disjoint points, simply because no 1-dimensional element is reducible to 0-dimensional element, so the assertion that Cantor set has Lebesgue measure 0 is false, and this fallacy is exactly the reflection of context-dependent-only reasoning on the result, which can't comprehend cross-contexts form like 1-dimensional element among 0-dimensional elements, which are context-dependent forms w.r.t it (by analogy, each point has a single location along the line, where the line does not have a single location w.r.t to any given point along it).
 
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jsfisher said:
If only you had something you could present to prove you case....

Something, that is, other than the misunderstanding of simple concepts, circular reasoning, contradictory statements, and accusations that it really is everyone else who have the failings you so clearly demonstrate.

Got anything like that?
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Hello, is there anybody at home to get the result of the following expression?: 1 - 0.999...[base 10] = 0.000...1[base 10] (where "...1" of 0.000...1 expression is the non-locality of the real-line that is simultaneously < AND = 1, which is a property that no point (locality) along the real-line has).

Until now there is no one at home to get it, exactly because only context-dependent reasoning is used.
 
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doronshadmi said:
Hello, is there anybody at home to get the result of the following expression?: 1 - 0.999...[base 10] = 0.000...1[base 10] (where "...1" of 0.000...1 expression is the non-locality of the real-line that is simultaneously < AND = 1, which is a property that no point (locality) along the real-line has).
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That is not a result. It is something you invented to cover your ignorance. It is also inconsistent with Arithmetic since it leads almost immediately to a contradiction.

It is interesting, though, that you cherish contradiction. That puts much of your spewage in a proper context.
 
jsfisher said:
That is not a result. It is something you invented to cover your ignorance. It is also inconsistent with Arithmetic since it leads almost immediately to a contradiction.

It is interesting, though, that you cherish contradiction. That puts much of your spewage in a proper context.
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It is not interesting, though, that you are limited to local-only reasoning, which gets non-locality as contradiction and therefore can't get non-local result as 0.000...1[base 10].

jsfisher said:
That puts much of your spewage in a proper context.
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jsfisher that is only puts much of your context-dependent-only "death by entropy" reasoning.
 
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doronshadmi said:
It is not interesting, though, that you are limited to local-only reasoning, which gets non-locality as contradiction and therefore can't get non-local result as 0.000...1[base 10].
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Well, yes, so far just about everything you have tried to present as "non-local" has led to a contradiction. Recognizing that it is contradictory isn't a limitation I have. Not seeing the contradiction, however, is definitely a limitation you have.

So, once again, Doron, you accuse others of limitations only you have.

Be the way, we have not forgotten, either, that you have been unable to define what this 0.000...1 notation nonsense is supposed to mean. Care to try again, or shall we just leave that on the pile of Doron's defined concept failures?
 
I am curious as to why people have encouraged doronshadmi by continuing to participate in this thread.

There is no longer any possibility of reaching him, or responding to any questions in a useful way. There is no chance that anyone will be led into error by his writings and need to be shown the way out. I don't think anything more can be learned from this. It hasn't been amusing for a very long time.

If people wish to continue, by all means do so, but I truly don't understand. Think of the time that you have invested in responding to his posts, and imagine how that time could have been spent otherwise.

Have a great day.
 
Complexity said:
I am curious as to why people have encouraged doronshadmi by continuing to participate in this thread.

There is no longer any possibility of reaching him, or responding to any questions in a useful way. There is no chance that anyone will be led into error by his writings and need to be shown the way out. I don't think anything more can be learned from this. It hasn't been amusing for a very long time.

If people wish to continue, by all means do so, but I truly don't understand. Think of the time that you have invested in responding to his posts, and imagine how that time could have been spent otherwise.

Have a great day.
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In a broad sense, anyone who keeps responding to Doron may not be regarded as an overly rational person, unless there are reasons that may not be apparent to a bystander. It's sort of similar to the situation where some theists would keep responding to the atheists and vice-versa. That exchange and the way it is done is a sorrowful display of God's abandonment of some of his children (lols), but some folks love to bicker and so they do.

You are limited to the local-only reasoning and therefore can't get the reasons behing this thread's continuum. How about that? LOL.
 
doronshadmi said:
( http://en.wikipedia.org/wiki/Lebesgue_measure )
|b−a| > 0 even if [a,b] is (according to traditional math) no more than a set of 0-dimensional elements.
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You've misinterpreted the meaning of the article. Just read this
In mathematics, Lebesgue integration, named after French mathematician Henri Lebesgue, refers to both the general theory of integration of a function with respect to a general measure, and to the specific case of integration of a function defined on a sub-domain of the real line or a higher dimensional Euclidean space with respect to the Lebesgue measure. This article focuses on the more general concept.
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http://en.wikipedia.org/wiki/Lebesgue_integral

and see this: http://en.wikipedia.org/wiki/File:RandLintegrals.png

Lebesque measure just sets the stage for a bit different integration technique of some unwieldy functions.

It can be done only under 1-dimensional\0-dimensional co-existence.
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Then do it.

The-J-Curve_blanksm.jpg


The 1-dim existence is represented by the curve with the length that you need to know, and the 0-dim existence is represented by the two endpoints. So you have the nice co-existence that you need to unleash the power of OM.
 
Complexity said:
I am curious as to why people have encouraged doronshadmi by continuing to participate in this thread.

There is no longer any possibility of reaching him, or responding to any questions in a useful way. There is no chance that anyone will be led into error by his writings and need to be shown the way out. I don't think anything more can be learned from this. It hasn't been amusing for a very long time.

If people wish to continue, by all means do so, but I truly don't understand. Think of the time that you have invested in responding to his posts, and imagine how that time could have been spent otherwise.

Have a great day.
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It amuses us, just as, presumably, it amuses you to post in a thread you're no longer interested in when you could have been doing something useful with that time.
 
zooterkin said:
It amuses us, just as, presumably, it amuses you to post in a thread you're no longer interested in when you could have been doing something useful with that time.
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Then I am in awe at your ability to stay in the game so long and still be amused. The only eternal-thread originator who continually provides me with entertainment is Bjarne, and I think that his cows are the thing that keep me coming back.

Doronshadmi needs some cows.
 
jsfisher said:
Well, yes, so far just about everything you have tried to present as "non-local" has led to a contradiction.
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Wrong.

So far just about everything you have tried to get as non-local by using locality, has led to a contradiction.

jsfisher said:
Be the way, we have not forgotten, either, that you have been unable to define what this 0.000...1 notation nonsense is supposed to mean. Care to try again, or shall we just leave that on the pile of Doron's defined concept failures?
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You are still missing http://www.internationalskeptics.com/forums/showpost.php?p=7338074&postcount=15847 .

Care to try again, or shall we just leave that on the pile of jsfisher's closed box failures?
 
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epix said:
You've misinterpreted the meaning of the article. Just read this

http://en.wikipedia.org/wiki/Lebesgue_integral

and see this: http://en.wikipedia.org/wiki/File:RandLintegrals.png

Lebesque measure just sets the stage for a bit different integration technique of some unwieldy functions.


Then do it.

[qimg]http://upload.wikimedia.org/wikipedia/en/1/15/The-J-Curve_blanksm.jpg[/qimg]

The 1-dim existence is represented by the curve with the length that you need to know, and the 0-dim existence is represented by the two endpoints. So you have the nice co-existence that you need to unleash the power of OM.
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epix, do you agree that your measured curve is 1-dim\0-dims co-existence?

Please answer only by yes or no.
 
doronshadmi said:
Wrong.

So far just about everything you have tried to get as non-local by using locality, has led to a contradiction.
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It has nothing to do with what I get. Once again, Doron, you accuse others of failings that are uniquely yours.

You are still missing http://www.internationalskeptics.com/forums/showpost.php?p=7338074&postcount=15847 .
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Didn't miss it at all. That would be were you asserted 1 and 0.999... represented different numbers and the difference was 0.000...1. That is also where you didn't say what number your undefined notation represented.

Everyone (except you) knows what the notation 0.999... represents. (It would be that well-know infinite sum of 9 times negative powers of 10.) No one (including you) knows what 0.000...1 is supposed to represent.
 
In mathematics, a Dedekind cut, named after Richard Dedekind, is a partition of the rational numbers into two non-empty parts A and B, such that all elements of A are less than all elements of B, and A contains no greatest element. The cut itself is, conceptually, the "gap" defined between A and B. In other words, A contains every rational number less than the cut, and B contains every rational number greater than the cut. The cut itself is in neither set.
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( 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.

So Dedekind's cuts are actually based of 1-dim\0-dims co-existence.

The Dedekind cut resolves the contradiction between the continuous nature of the number line continuum and the discrete nature of the numbers themselves.
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( http://en.wikipedia.org/wiki/Dedekind_cut )

The Dedekind cut resolves nothing.

1-dim\0-dims co-existence has no contradiction because no amount of 0-dims along 1-dim completely covers it exactly because the power of the continuum is at least a 1-dim element, which is notated by < between any arbitrary closer pair of 0-dims along it.

Traditional Math invents and solves problems that do not exist in the first place, in this case.
 
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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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