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Deeper than primes

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In other words, the real-line is not regular enough to be described in Euclidean terms, exactly because it is the complex result of the co-existence of (smaller OR greater) AND smallest, which has strange attractor (smaller OR greater are irreducible to the smallest).
Doron, it takes a few clicks for anyone passing by to find out that you're trying to blend existing terminologies that describe certain processes with your own terminologies that describe things absolutely not related to anything outside your phantasmagorical constructs.

There has been an attempt to challenge your law of irreducibility.
http://en.wikipedia.org/wiki/Null_vector

You must rearm and attack at dawn . . .
 
So it is smaller than what it is smaller than? Talk about profound insights.

Would that be a multiplicity of “greater elements” that it is smaller than?

“all greater elements”? Is your set of ““all greater elements” complete or incomplete? If it is complete then your claim about sets being incomplete is false. If it is not complete then your claim of “all greater elements” is false. So which one are you wrong about Doron. Again you simply remain the staunchest opponent of just your own notions.

Since any given infinite collection has successors (immediate or not) as its inherent property, it is incomplete w.r.t fullness, which has no successor (immediate or not).

So only fullness can be considered as actual infinity (notated as ), where any collection (which is an existence only at the level of multiplicity, and generally notated as ∞) is only a potential infinity w.r.t .

Your reasoning, The Man, is closed under ∞ and therefore can't comprehend as the strongest realm.

Furthermore, your reasoning is closed under existing elements, and therefore can't comprehend nothing (that has no predecessor) as the weakest realm.

EDIT:

Moreover, your reasoning can't comprehend Unity as the realm beyond expression of any kind.
 
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Doron, it takes a few clicks for anyone passing by to find out that you're trying to blend existing terminologies that describe certain processes with your own terminologies that describe things absolutely not related to anything outside your phantasmagorical constructs.

There has been an attempt to challenge your law of irreducibility.
http://en.wikipedia.org/wiki/Null_vector

You must rearm and attack at dawn . . .
epix, it takes no clicks for anyone passing by to find out that your reasoning is closed under the concept of collection of localities.
 
Both what “are considered”? Most of us already know that English is not your first language. So again for your edification “both” denotes, well, both while “or” explicitly indicates either, Hence the inconsistency.

http://www.internationalskeptics.com/forums/showpost.php?p=7161892&postcount=15365

No doron a difference is called “difference” and interval is called “interval” because they are, well, different.
EDIT:

It is meaningless exactly as to say that: " difference is called “difference” and interval is called “interval” because they are, well, intervals. ", because in both cases a circular reasoning is used (the defined is a factor of the definition).

If Complexity is considered, then in both cases, there must be co-existence of more than one thing, such that the co-exiting things save their ids under the co-existence, and therefore they are considered as the building-blocks, which are used as the agents of Unity that enable Complexity.

These agents are the irreducibility of the smaller to the smallest, and the non-extendability of the smallest to the smaller.

The realms beyond Complexity are Nothing and Fullness (Nothing is too weak for the co-existence of the smaller AND the smallest, and Fullness is too strong for the co-existence of the smaller AND the smallest.

The realm beyond Nothing AND Fullness is Unity, which is beyond expression of any kind.

That you simply want to conflate difference with interval, in spite of the fact that there is no difference in some intervals and there is no interval resulting from some differences, is just your problem.
Your reasoning is closed under the complex result of the co-existence of the smaller AND the smallest).

By using it you are unable to comprehend the smaller AND the smallest) building-blocks of Complexity, you are unable to comprehend Nothing as the weak limit of Complexity or Fullness as the strong limit of Complexity, and you are unable to comprehend Unity as the source of any expression, which is beyond any expression.

Since I have certainly never asserted that I “understand Collection only in terms of list” and have quite plainly asserted otherwise. It remains simply you who is lying to yourself and still trying to lie to us.
You still do not generalize the considered subject to the level of Collection.

Your inability to understand that your “essential different ids” are essential only to you and your self-contradictory nonsense is why you will spend another twenty just convincing yourself they are essential. Indeed not a very "profound" insight Doron but one sadly quite evident.
You are invited to define Multiplicity by using only the smallest.

What do you mean “without the co-existence of smaller AND smallest”?

The following definition …

http://dictionary.reference.com/browse/multiplicity

Makes no reference to your “co-existence of smaller AND smallest”, though it doesn’t specifically preclude your “co-existence” either. So you’re going to have to try to be more specific.
Another example of your boxes reasoning, which is based only on already agreed definitions of the considered subjects, and therefore naturally blocks itself from any re-consideration of them. What You Choose To See Is What You Get (WYCTSIWYG).

Your are still deliberately ignoring the fact that you again assert you simply have no basis even just under your own assertions to claim they are independent.
The Man, again please define Multiplicity without the co-existence of at least two building-blocks.

Then your independent “non-locality” is impossible as it is more they one location and is specifically by your own assertion dependent on your “locality”.
The Man please show me a 0-dim element that exists in more than one location, and also please show me a 1-dim element that exists in only one location.
 
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That's just another of the many things you simply made up. Things you make up are seldom true no matter how much you want to believe them.
jsfisher, please define some fractal by not using even a single point (known also as the smallest element).
 
epix, it takes no clicks for anyone passing by to find out that your reasoning is closed under the concept of collection of localities.

Meet your irreducible nightmare:

pic398.gif


fncom-03-001-i038.gif


1c6978fc972b3cf649bd9c4429839a64.png


ZeroVector_1000.gif


math-86b0265ed0f2d5219411c60dd426ad48.png


2225194-2.png



shady_point_cemetery_entrance.jpg
 
Since any given infinite collection has successors (immediate or not) as its inherent property, it is incomplete w.r.t fullness, which has no successor (immediate or not).

Again a set that is closed under and operation of succession has no successors that are not also members of that set and all sets by definition are complete (they have all and only the members they are defined to have). Once again your are insisting that a set is only complete if it includes members that you claim yourself that set does not include. This simply makes your notion of a 'complete set' self-contradictory.


So only fullness can be considered as actual infinity (notated as ), where any collection (which is an existence only at the level of multiplicity, and generally notated as ∞) is only a potential infinity w.r.t .

Are you claiming there is no “multiplicity” in your “fullness”?

Your reasoning, The Man, is closed under ∞ and therefore can't comprehend as the strongest realm.

Furthermore, your reasoning is closed under existing elements, and therefore can't comprehend nothing (that has no predecessor) as the weakest realm.


Stop simply trying to pawn off aspects of your own failed reasoning on to others.

EDIT:

Moreover, your reasoning can't comprehend Unity as the realm beyond expression of any kind.

So you are specifically claiming that this “Unity” “realm” of yours is simply beyond your ability to express in any representative way. This simply means that you know what the rest of us know, that you assertions simply don’t and can’t express what you want them to. So are you just going to waste another 20 years trying to express what you claim you simply can’t or move onto goals that at least you think you are obtainable?
 

What of it?

EDIT:

It is meaningless exactly as to say that: " difference is called “difference” and interval is called “interval” because they are, well, intervals. ", because in both cases a circular reasoning is used (the defined is a factor of the definition).

I didn't define either Doron just pointed out again that they are different. A fact you evidently simply want to deliberatly ignore.

If Complexity is considered, then in both cases, there must be co-existence of more than one thing, such that the co-exiting things save their ids under the co-existence, and therefore they are considered as the building-blocks, which are used as the agents of Unity that enable Complexity.

That would be the “Unity” that you calm you can’t accurately express “that enable” your “Complexity”? How unfortunate for you.

These agents are the irreducibility of the smaller to the smallest, and the non-extendability of the smallest to the smaller.

The realms beyond Complexity are Nothing and Fullness (Nothing is too weak for the co-existence of the smaller AND the smallest, and Fullness is too strong for the co-existence of the smaller AND the smallest.

The realm beyond Nothing AND Fullness is Unity, which is beyond expression of any kind.

“Oh waiter, can I get more gibberish croutons in this word salad?”

Your reasoning is closed under the complex result of the co-existence of the smaller AND the smallest).

Again stop simply trying to posit aspects of your own failed reasoning on to others.

By using it you are unable to comprehend the smaller AND the smallest) building-blocks of Complexity, you are unable to comprehend Nothing as the weak limit of Complexity or Fullness as the strong limit of Complexity, and you are unable to comprehend Unity as the source of any expression, which is beyond any expression.

Actually Doron we all comprehend it, you are unable by your own assertions to accurately express what you mean, as a result you assert nonsensical gibberish.

You still do not generalize the considered subject to the level of Collection.

The fact that sets, lists and classes are collections still doesn’t make a set a list. Another fact you seemingly just want to deliberatly ignore.

You are invited to define Multiplicity by using only the smallest.

Your are invited to do so yourself if that is what you want.

Another example of your boxes reasoning, which is based only on already agreed definitions of the considered subjects, and therefore naturally blocks itself from any re-consideration of them. What You Choose To See Is What You Get (WYCTSIWYG).

Too bad that spending twenty years trying to express what you claim is beyond any expression hasn’t worked out so well for you. People communicate because they can agree on the meanings of words. Since you have claimed your “Unity” is not expressible your inability to communicate it effectivly doesn’t seem to matter.

The Man, again please define Multiplicity without the co-existence of at least two building-blocks.

Again? I gave you the definition you asked for, blame your “unity” for your inability to communicate what you actually wanted.



The Man please show me a 0-dim element that exists in more than one location, and also please show me a 1-dim element that exists in only one location.

Doron no one has claimed that there is a singular “0-dim element that exists in more than one location” so show yourself that. However, as you claim your line to be indivisible then your “1-dim element” “exists in only one location”. A location does not have to be constrained to a point (and we have been over that before).
 
A location does not have to be constrained to a point
A point is the minimal expression of locality under non-locality\locality co-existence, where a line segment is the minimal expression of non-locality under co-existence.

Yet there are non-minimal expressions of non-locality\locality co-existence among smaller (localities under co-existence) and bigger (non-localities under co-existence) dimensions.

The smallest dimension (notated by 0) is the immediate (and under non-locality\locality co-existence) successor of Nothing (which is non-existence and does not have notation) and bigger dimensions are non-immediate (notated by x (such that 0 < x ≤ ∞) and under non-locality\locality co-existence) predecessors of Fullness (notated by and beyond co-existence and non-existence).

Beyond Nothing, Locality\Non-locality co-existence and Fullness there is the realm of Unity, where no degrees of any kind are expressible.
 
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Meet your irreducible nightmare:

[qimg]http://www.westone.wa.gov.au/k-12lrcd/learning_areas/maths/mathsp3C/001_vectors/images/pic398.gif[/qimg]

[qimg]http://www.frontiersin.org/files/TempImages/imagecache/323_fncom-03-001/images/image_n/fncom-03-001-i038.gif[/qimg]

[qimg]http://upload.wikimedia.org/math/1/c/6/1c6978fc972b3cf649bd9c4429839a64.png[/qimg]

[qimg]http://mathworld.wolfram.com/images/eps-gif/ZeroVector_1000.gif[/qimg]

[qimg]http://dictionary.sensagent.com/wiki/images/math/86/math-86b0265ed0f2d5219411c60dd426ad48.png[/qimg]

[qimg]http://www.physicsforums.com/latex_images/22/2225194-2.png[/qimg]


[qimg]http://freepages.genealogy.rootsweb.ancestry.com/~ajobebrown/duncan/shady_point_cemetery_entrance.jpg[/qimg]

x is a placeholder.

x>0

x-x = 0 exactly because x>0

EDIT:

if x=0 then the result is also 0, but then the irreducibility of x to 0 and the non-extendability of 0 to x, is not considered.
 
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So start by educating yourself, because all you are doing in this thread is simply repeating on the agreed knowledge of the considered subject.


Strangely, though, this thing you so incompetently belittle continues to work, providing useful and meaningful results continually. And the contradictory buffoonery you utter has nothing to show for itself by gratuitous hand-waving.
 
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