Deeper than primes - Continuation

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The collection of natural numbers is clopen (where clopen, by a narrow view, means that the collection has minimal member but not maximal member).

First, let us use the narrow view of the clopen concept:

We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length, then we cut the circle at a point named 1, and transform the curved form into a clopen system of a straight line with a finite length (it is a clopen system because after the cut only one edge of the finite straight line is considered as the point that represent number 1).

Now the modular arithmetic form of all posible natural numbers along it, is rolled along the clopen finite straight line, where each tangent point is a 1-to-1 correspondence between the finite modular (circle) arithmetic form and the straight arithmetic form.

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Now, let us use the generalized view of the clopen concept:

Since both systems are clopen (by generalization no number is taken twice at each system), their accurate infinite cardinality is not satisfied.

Furthermore (now we are generalizing the notion of clopen by avoiding number's duplication along both circular and straight finite length forms), since a point along finite length (whether it has circular or straight form) represents one an only one number, then the clopen state holds for both circular and straight finite length forms, such that the accurate cardinality of Q or R is not satisfied.

Moreover, the order of the numbers, which are represented by points along both circular and straight finite length forms has no impact on the fact that both forms are clopen, and they are clopen because the cut is done at any given arbitrary point, which avoids number's duplication along both circular and straight finite length forms.

Since being clopen is a fact among any collection of distinct members, such collections (where their order is insignificant) do not have accurate infinite cardinality.
 
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realpaladin said:
That was before you started walking. From the moment you spouted gobbledigook again he clicked his ruby slippers and was gone.
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He does not use mathematical concepts as a part of his replies, so your argument is irrelevant.
 
doronshadmi said:
The collection of natural numbers is clopen
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Except it isn't. Don't understand the term, clopen, either, do you?

We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length...
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Oh, Doron, you skipped all the interesting details. Please show us exactly what you mean by "modular arithmetic form" since it is likely your usage is, well, non-standard. Use modulo 2. That would be the simplest for an example.
 
realpaladin said:
I am refraining from answering as well, since we are now in Religion and Philosophy and I am eager to see Doron and his sidekick Punshhh discuss some unity stuff.

But I stand by my prediction that Punshhh will be going the way all of Doron's sidekicks go... they support him for a bit but then mosey off when he starts following the yellow brick road again.
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I have nothing to discuss with Doron for we are in agreement.
 
punshhh said:
I have nothing to discuss with Doron for we are in agreement.
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That made me laugh out loud too. In agreement about what? Explain Doron's theories to me and I don't mean his claim to be at one with unity. Explain his maths to me. Translate this gobbledygook for me please.

''We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length, then we cut the circle at a point named 1, and transform the curved form into a clopen system of a straight line with a finite length (it is a clopen system because after the cut only one edge of the finite straight line is considered as the point that represent number 1)''
 
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Some traditional mathematician skips all the interesting details, when he\she asks to represent infinitely many distinct members by finitely many distinct members (for example: modulo 2 is some case of a finite field), exactly because he\she does not understand that infinitely many distinct members along a finite length are clopen system, whether this finite length is a circle or a straight line.
 
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doronshadmi said:
Some traditional mathematician skips all the interesting details, when he\she asks to represent infinitely many distinct members by finitely many distinct members.
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Ah! More evasion. We understand. You can't show your work because it doesn't work. Here, let me help you get started:

Arithmetic modulo 2 gives rise to two equivalence classes which we can represent using the conventional representative from each class, those being 0 and 1. We can map the natural number 0 to "modular arithmetic form" 0, and we can map the natural number 1 to "modular arithmetic form" 1.

There! I've got you started. Now, you try. What will be the mapping for natural number 2 in this bijection you claim exists?


You aren't ever going to get back to the original issue, either, are you? You know, where you asked that perfectly meaningless question, meaningless on two counts. You continue to distance yourself from that bit of stupidity on your part.
 
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doronshadmi said:
As can be seen, traditional mathematics' modular arithmetic is restricted to finite amount of distinct members (some case of a finite field) along a circle.

As a result it can't deal with clopen systems as observed in http://www.internationalskeptics.com/forums/showpost.php?p=8074095&postcount=561 .
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More evasion, but at least you continue to make it abundantly clear that you have virtually no understanding of Mathematics. A vocabulary of misused and invented terms is no substitute for knowledge.

Nonetheless, carry on. You've wasted all these many years of your life on your fantasy; without anything rational to fill the void you may as well continue with it.
 
An evasion is noted each time Traditional Mathematics has to deal with its own limitations.

The slogan "understanding of Mathematics" is actually being closed under the limitations of Traditional Mathematics.

A limited vocabulary and the inability to re-define notions is no substitute for knowledge.
 
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Traditional Mathematics is the mastery of verbal_only anti-evolutionist embalmed definitions.
 
doronshadmi said:
Traditional Mathematics is the mastery of verbal_only anti-evolutionist embalmed definitions.
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Doron, this really is silly. You are acting like a kindergarten pupil on the playground. "Am not!" "Are too!"

You are going out of your way to avoid communication. You know it. We know it. We know you know it. And you know we know you know it.

Stop pretending.

If you have something to say, say it. But leave out the gibberish and the Doron-special meaningless terminology. If your goal really is to expose and discuss whatever revelation you have, you stupid antics are completely out of phase with that goal.
 
Please look at the following diagrams ( http://www.math.rutgers.edu/~erowland/polygons-project.html ):

polygons-diagonals.gif


The distinct points on the perimeter are defined as long as the cardinality of the connected lines at each point is smaller by 1 than the cardinality of the points.

By pushing this system into actual infinity, no distinct points are defined anymore exactly because at actual infinity there is the power of the continuum, observed as 1-dimesional curved line (known as circle, in this case) which is not a collection of lower spaces (points) or sub-spaces (segments of curves).
 
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Traditional Mathematics can't rid of its traditional dogma in order to develop actual communication, because its dogma is context-dependent-only framework (no cross-contexts form is found).
 
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jsfisher said:
Doron, this really is silly. You are acting like a kindergarten pupil on the playground. "Am not!" "Are too!"

You are going out of your way to avoid communication. You know it. We know it. We know you know it. And you know we know you know it.

Stop pretending.

If you have something to say, say it. But leave out the gibberish and the Doron-special meaningless terminology. If your goal really is to expose and discuss whatever revelation you have, you stupid antics are completely out of phase with that goal.
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doronshadmi said:
Traditional Mathematics can't rid of its traditional dogma in order to develop actual communication, because its dogma is context-dependent-only framework (no cross-contexts form is found).
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Understood. You have no interest in communication.
 
Please look at the following diagram ( http://mathoverflow.net/questions/8846/proofs-without-words done by Jason Dyer ):

proofwowords.png


Verbal_symbolic-only minds take it a a proof without words that "The cardinality of the real number line is the same as a finite open interval of the real number line."

According to Traditional Mathematics a given length is totally covered by points. In this case Traditional Mathematics can't explain how a collection of the same cardinality, which totally covers a given length, can define different lengths.
 
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doronshadmi said:
Please look at the following diagram ( http://mathoverflow.net/questions/8846/proofs-without-words done by Jason Dyer ):

Verbal_symbolic-only minds take it a a proof without words that "The cardinality of the real number line is the same as a finite open interval of the real number line."

According to Traditional Mathematics a given length is totally covered by points. In this case Traditional Mathematics can't explain how a collection of the same cardinality, which totally covers a given length, can define different lengths.
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And, had you read all the comments you would have noticed that proofs without words are usually useless and only usefull in very specific cases; cases that have been defined by... wait for it... words and symbols.

Because, Doron, in the first thread we all have already shown that even symbols *and* graphics are not fitting in anything you say.

This has been done. Maybe your mind does not reach back over the years, but my notes pinned to this thread do.

You are unable to prove a single *COHERENT* thing. You jump back and forth just trying to find something to 'invalidate' each and every participant in this thread, but are not able to do a single thing yourself.

And, we already had this exact same moment over and over again, in the end, you get nothing out of it.

Making everybody in this forum 'be wrong' does not make you right. This compulsive kibbitzing is doing nothing for your case.

I sincerely doubt that anyone in this thread is losing more time on what you think than it takes to read your posts and then post a bemused reply themselves.

So, again... make a coherent story, stick to it and prove it. I won't leave this thread, and probably jsfisher etc. won't either. But it is not that we feel threatened, it is, as the german term goes, schadenfreude of seeing someone make a trainwreck of himself.

Come on, do better than google 10 minutes and post the first thing that seems to agree with you, but doesn't
 
doronshadmi said:
This claim is equivalent to your claim that punshhh and me are in disagreement on the discussed subject.
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Indeed it is.

Let's get back to the subject at hand: Deeper than primes.
 
Please look at the following part, taken from http://www.math.vanderbilt.edu/~schectex/courses/thereals/ :


Getting rid of the pictures


"The "point on a line" answer is not a fully satisfactory answer, because it is not axiomatic or algebraic. It relies on pictures that we don't really understand. For instance, the set of real numbers and the set of rational numbers have essentially the same picture, but their algebraic properties differ in ways that are very important for analysts.

Imagine studying that picture of a line under a super microscope. If you could magnify the line at a very high power -- say at a magnification of a googolplex, or better yet a magnification of infinity -- would it still look the same? Or would you see a row of dots separated by spaces, like the dots in a picture in a newspaper? (It turns out that, in some sense, the real numbers would still look like a line under infinite magnification, but the rational numbers would be dots separated by spaces. But that is only a vague and intuitive statement, not anything precise that we can use in proofs.)

The only way to get rigorous answers to these questions is to set up a very careful system of axioms about geometry ... but that amounts to the same thing as setting up a careful set of axioms about the algebraic properties of the real numbers. It turns out that the latter is a little easier, so we may as well concentrate on the algebraic aspects of the situation. To answer questions like this, ultimately we have to get away from the pictures; we have to understand the real numbers entirely in terms of formulas."

This is a common example of how Traditional Mathematics can't use verbal_symbolic AND visual_spatial skills, in order to actually understand the real-line ( as done by Organic Mathematics, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=7952072&postcount=362 ).
 
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realpaladin said:
Indeed it is.

Let's get back to the subject at hand: Deeper than primes.
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The subject at hand is that the power of the continuum is not satisfied in terms of collection, and this knowledge is deeper than the knowledge about primes, because it has a direct influence on our understanding of the concept of Entropy (the inability of collection of lower spaces or sub-spaces to completely cover a given space > 0, is resulted by non-entropic and therefore ever-developed (abstract or physical) realm).

As for you, you can't get, for example, http://www.internationalskeptics.com/forums/showpost.php?p=8059077&postcount=473 .
 
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Ok, now let's use new notations on order to define the novel notions, as follows:

;||; = the cardinality of NOthing (that has no predecessor).

|;;| = the cardinality of YESthing (that has no successor).

;|c0|; = the cardinality of 0-space(s) do not have the power of the continuum.

;|c1,c0|; = the cardinality of 1-space has the power of the continuum, but the cardinality of 0-spaces on it do not have the power of the continuum.

;|c2,c1,c0|; = the cardinality of 2-space has the power of the continuum, but the cardinality of 1-spaces and 0-spaces on it do not have the power of the continuum.

;|c3,c2,c1,c0|; = the cardinality of 3-space has the power of the continuum, but the cardinality of 2-spaces,1-spaces and 0-spaces on it do not have the power of the continuum.

...

etc. ad infinitum ... where no space > 0 has the power of the continuum of YESthing (that has no successor).

Beyond these powers there is the thing, which is the Unity beyond polychotomy.
 
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Let's improve the formal novel system:

;||; = the cardinality of NOthing (that has no predecessor).

|;;| = the cardinality of YESthing (that has no successor).

Beyond these states there is the thing, which is the Unity beyond polychotomy.

The power of continuum is defined as the ability of a given space to be at AND beyond (not at) the domain of given lower space(s) or sub-space(s) (where sub-space(s) is\are a mixture of a given space and lower spaces, associated by Unity (by the thing)).

;|c0|; = the cardinality of 0-space does not have the power of the continuum.

;|c1,c0|; = the cardinality of 1-space has the power of the continuum, but the cardinality of 0-spaces on it do not have the power of the continuum.

;|c2,c1,c0|; = the cardinality of 2-space has the power of the continuum, but the cardinality of 1-spaces and 0-spaces on it do not have the power of the continuum.

;|c3,c2,c1,c0|; = the cardinality of 3-space has the power of the continuum, but the cardinality of 2-spaces,1-spaces and 0-spaces on it do not have the power of the continuum.

...

etc. ad infinitum ... where no space > 0 has the power of the continuum of YESthing (that has no successor).

In general, no collection of lower spaces or sub-spaces, has the power of the continuum of a given space.
 
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punshhh said:
I'm glad to effortlessly provide entertainment.


Think about unity, what could Doron and myself not agree on about unity?
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punshhh, by only thinking about Unity, realpaladin is not actually at Unity, so any answer that is given by being trapped at the level of thoughts is irrelevant.
 
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punshhh said:
I'm glad to effortlessly provide entertainment.

Think about unity, what could Doron and myself not agree on about unity?
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What could you agree on?
 
punshhh said:
I'm glad to effortlessly provide entertainment.


Think about unity, what could Doron and myself not agree on about unity?
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No idea, it's a woo concept so I'll leave it to you to explain it. What does he mean by being at Unity? Are you there too?
 
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