Deeper than primes - Continuation

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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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