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Deeper than primes

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zooterkin said:
Ah, got it.
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Translation: "I can't get your proof without words ( including the following: )"

doronshadmi said:
X is an accurate value, called a sum.

(2a+2b+2c+2d+...) is an inaccurate value < X, and it is called (and here comes a novel concept) a fog.

Fogs are only approach to a given sum (what is called by you a limit).

For example: pi is a sum, and it is used by Standard Math as the limit of fog 3.14...[base 10], where fog 3.14...[base 10] < pi (fog 3.14...[base 10] only approaches sum pi).

In order to reach pi, one simply "jumps" form any arbitrary chosen scale level straight to sum pi, but then fog 3.14...[base 10] < pi is not found anymore, and we get a sum, which is based on finitely many segments AND points that have sum pi.

This novel reasoning about infinite convergent series is clearly demonstrated in http://www.internationalskeptics.com/forums/showpost.php?p=5721761&postcount=9104.

In other words, sums are local numbers, and fogs are non-local numbers.

By OM the place value method is a fog if infinitely many scale levels are involved.

By Standard Math the place value method is a representation of a sum (fogs are not found under the Standard framework).

Since Standard Math paradigm does not deal with fogs, then X can't be but a sum.

By using the limited reasoning, one simply can't get (2a+2b+2c+2d+...) as a fog (called also a non-local number, under OM).
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doronshadmi said:
Translation: "I can't get your proof without words ( including the following: )"
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I wasn't asking for one of your 'proofs', I was asking for a definition of your latest term, 'fog'. You have yet to provide one.

ETA: Oh, and your reply included a whole bunch of words (so much for 'proof without words') from a completely different post than the one you originally referred me to, but you still try to pretend it's my fault that I don't find any meaning in the gibberish. Still no definition of 'fog', though.
 
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zooterkin said:
I wasn't asking for one of your 'proofs', I was asking for a definition of your latest term, 'fog'. You have yet to provide one.

ETA: Oh, and your reply included a whole bunch of words (so much for 'proof without words') from a completely different post than the one you originally referred me to, but you still try to pretend it's my fault that I don't find any meaning in the gibberish. Still no definition of 'fog', though.
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EDIT:

zooterkin, if you really follow my posts, you will find this:

k < x < n

A fog is the infinite irreducibility of x to k or the infinite non-increaseability of x to n
 
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doronshadmi said:
What You See Is What You Get sympathic, and you do not see (or in your words: "More useless gibberish").
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Please stop deluding yourself. Your gibberish is no more than just, well... gibberish. Seeing things that are not there is not a healthy symptom.
 
doronshadmi said:
EDIT:

zooterkin, if you really follow my posts, you will find this:

k < x < n

A fog is the infinite irreducibility of x to k or the infinite non-increaseability of x to n
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Well, that's completely different from what was there the last time i looked at that post. Doesn't make any more sense, mind. Exactly what is foggy about two values being different?
 
zooterkin said:
Well, that's completely different from what was there the last time i looked at that post. Doesn't make any more sense, mind. Exactly what is foggy about two values being different?
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x is a a placeholder for a fog, for example: fog S=(0.9+0.09+0.009+0.0009+...[base 10]) which is < than sum 1 by fog 0.000...1[base 10]

In the case of infinite non-increaseability x is a placeholder for fog S and n is a placeholder for sum 1

In the case of infinite irreducibility x is a placeholder for fog 0.000...1[base 10] and k is a placeholder for sum 0
 
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doronshadmi said:
x is a a placeholder for a fog, for example: fog S=(0.9+0.09+0.009+0.0009+...[base 10]) which is < than sum 1 by fog 0.000...1[base 10]

In the case of infinite non-increaseability x is a placeholder for fog S and n is a placeholder for sum 1

In the case of infinite irreducibility x is a placeholder for fog 0.000...1[base 10] and k is a placeholder for sum 0
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I think you have completely overlooked the cyclone of S occluded by the partly cloudy x. (Highs in the mid-60's with a 30% chance of rain in non-local areas.)
 
I am amazed that there are now 234 pages of this drek.

I was attracted only by one of the post titles - something about Deeper than primes...

Silly rabbits! Nothing is deeper than primes.
 
doronshadmi said:
The Man you apparently fail to realize that infinite series of added sums is not itself a sum, exactly as a collection of all oranges is not itself an orange.
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Once again Doron you apparently fail to relies that “a collection of all oranges” is “not itself an orange”, because it’s “a collection of all oranges”. Just as an “infinite series of added sums is not itself a sum” because it is “an “infinite series of added sums”. Howeevr such a series can have a sum. You are the only one trying to conflate a “collection of all oranges” with an orange or an “infinite series of added sums” with the sum of that series.

doronshadmi said:
Actually S=(2a+2b+2c+2d+...) < X exactly because the two different endpoints can’t be reduced into a single point, and this irreducibility is based on the fact that X>0 is a constant upon infinitely many bended levels, that are irreducible to 0.
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Once again that brings us to a circle. In X and Y coordinates a circle starts and ends at the same point. In polar coordinates the circle starts at zero degrees and ends at 360 with the same R. Is that your whole problem that you simply do not understand coordinates and how different reference frames give you different coordinates for what might even be the same point is some given reference frame?

doronshadmi said:
The generalization here is the irreducibility of a non-local element (which its minimal representation is a 1-dim element) into a local element (which its minimal representation is a 0-dim element).
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Well as your “belongs to AND does not belong to” reduces to a simple contradiction, I can certainly understand why you want to claim your “non-local element” “generalization” to be, well, ‘irreducible’.

doronshadmi said:
Please look at the non-local green elements of the following diagram:

[qimg]http://farm3.static.flickr.com/2794/4464201033_30e7dbd8d4_o.jpg[/qimg]
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“non-local green elements”? Obviously you were able to not only localize them, but also give them finite and “fixed” lengths for each iteration (otherwise you could not have drawn them).


doronshadmi said:
It is obvious that the collection of all infinitely many convergent triangles, where each one of them has a non-local green side, are not reducible into a single point.

By following this fact, it is immediately and unconditionally understood that S=(2a+2b+2c+2d+...) < X
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You do understand that a triangle converges at three, well, points, don’t you (that’s what makes it a triangle)? You do understand that your “green side” is always local to your triangle, don’t you (otherwise it would not be a side of your triangle)?

Oh look, we finally have Doron defining a line (his green side of his triangle) by points (his “two different endpoints”). So what happens when there is no difference in points? Well it either ain’t a line and is just a point or it is some closed curve like a circle (or other geometric figure) that starts and ends at some singular point in one reference frame, but like a circle may start and end at different points in some other reference frame. Once again Doron you are the only one trying to conflate the labels we ascribe to some point or points with that point or points themselves. The labeling convention depends upon the reference frame being used which is just some particular convention for labeling points in some space.
 
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The Man said:
The labeling convention depends upon the reference frame being used which is just some particular convention for labeling points in some space.
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Here you fail, because a space is not less than the linkage of local element like a single point and a non-local element, like single line (closed or not)

The point belongs XOR does not belong w.r.t a given line.

The line belongs AND does not belong w.r.t a given point.

The contradiction is a direct result of the understanding of that linkage only from its local (point) aspect.

The rest of your post is based on this local-only reasoning of a considered space, and What You See Is What You Get, which by this local-only reasoning it can't be but a contradiction.
 
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