Deeper than primes

[doronshadmi]

“both list or set,”? “or” is not consistent with “both”.

Unless both are considered.

Again what is your “interval” between the letters A and B in the alphabet?

It is called difference. If there is nothing between A and B, the result is one and only one thing simply because "there is nothing between A and B" is equivalent to ""there is no difference between A and B".

Your ridiculous and self-contradictory assertions still do not constitute facts.

The ridiculous and self-contradictory is the reflection of your only-context-dependent reasoning, when it is used to comprehend a reasoning that uses cross-contexts reasoning in addition to context-dependent reasoning.

Once again I have made no assertions that “interval is valued only in terms of physical realm” nor requiring a “metric-space” and have repeatedly informed you of this fact, so stop simply lying.

You are lying to yourself by understand Collection only in terms of list.

Now a physical collection, like my collection of ELP albums and CD's has certain physical constraints, much like a list.

Your inability to understand the essential different ids of the smaller AND smallest under co-existence, is resulted by your misunderstanding of the concept of Collection

..." the concept of collection" is just, well, a concept. ...

This is really some "profound" insight of you, The Man.

Doron “multiplicity is involved” and required by your “singular line segment that exist at least in more than one location” which of course also requires your “0-dim element” that you call “location”. So the only one jumping all over the place in your nonsense assertions is still just you.

Doron you “do not comprehend” your own “non-locality (smaller) as a building-block in addition to locality (smallest) under co-existence, which is resulted by multiplicity.” nonsensical and self contradictory assertions.

You are invited to define multiplicity without the co-existence of smaller AND smallest.

“(smaller)”? Smaller than what? Without your “multiplicity” what can it be smaller than? Your “non-locality (smaller)” also by your own assertions specifically requires “more than one location” which of course requires your “locality (smallest)”. So the lack of comprehension, even just about your own nonsense assertions, remains demonstrably yours

You are still missing the fact that non-locality and locality are understood as such only under their co-existence.

Without this co-existence Multiplicity is impossible, and the observed complexity does not exist.

Doron you still just can’t comprehend that your “Philosophy” of simply making up self-contradictory nonsense and calling it “fundamentals” isn’t “theoretical or practical research” of any subject. The banalities remain simply and entirely yours.

The self-contradictory nonsense is entirely the result of the reflection of your only-context-dependent reasoning, when it is used to comprehend a reasoning that uses cross-contexts reasoning in addition to context-dependent reasoning.

 

[zooterkin]

Unless both are are considered.

In English, that is denoted by 'and', not 'or'.

 

[doronshadmi]

Mandelbrot set and Koch fractal don't live under one roof:

They are both based on the principle of self similarity over scales, which is a generalization that (according to your reply) you don't comprehend.

 

[doronshadmi]

The options in the interpretation are numerous and as always frightening.

The result of the co-existence of at least smaller AND at most smallest, is infinite complexity.

 

[doronshadmi]

In English, that is denoted by 'and', not 'or'.

Ok, thank you zooterkin.

As you know OR is AND (T,T-->T) + XOR (T,F-->T ; F,T-->T).

So let it be list AND (T,T-->T) set.

 

[epix]

Yes there are infinitely many distinct points (where a point is the smallest element) [...]

Can you disclose which and what are the dimensions that qualify the point to be the smallest element?

 

[doronshadmi]

It implies to me that those at least smaller elements are actually smaller than those smallest elements

Wrong implication, because being at least smaller means that X can't be the smallest, no matter how infinitely many reductions are done.

If X is at most smallest it can't be smaller, no matter how infinitely many extensions are done.

 

[doronshadmi]

Can you disclose which and what are the dimensions that qualify the point to be the smallest element?

EDIT:

Exactly 0 dimension. 1 dimension is irreducible to 0 dimension and this irreducibility defines it as at least smaller (where 0 dimension is the smallest) under the co-existence of smaller AND smallest.

 

[epix]

They are both based on the principle of self similarity over scales, which is a generalization that (according to your reply) you don't comprehend.

If you could comprehend both generating formulas and their iteration, then you would see not only the difference between those two objects but most importantly you would see no traces of "Smaller" and "Smallest" -- the two barbarian tribes that try to invade the civilized math world. And that's the point. You said "if you zoom in . . ." but never did.

 

[epix]

The result of the co-existence of at least smaller AND at most smallest, is infinite complexity.

Sounds familiar . . .

Each inheritance is to be distributed by lot among the larger AND smaller groups.
Numbers 26:56

 

[epix]

Wrong implication, because being at least smaller means that X can't be the smallest, no matter how infinitely many reductions are done.

If X is at most smallest it can't be smaller, no matter how infinitely many extensions are done.

Was I right or was I right? LOL. The Doronian space where reduction and extension live in harmony despite being opposites teems with objects of peculiar properties to say "the least at most."

So X can't be smaller no matter how infinitely many extensions are done. Maybe it's because extension is the opposite to reduction, and during the process of extension things tend to be longer and not shorter, as it is happening in your "framework."


the least at most
the most at least
north is down
and left is east

less at more
and more at less
down is Loch
and up is Ness

creature feature
framework poof
if up is down
then where's the roof?

arrows, arrows
point me out
point the left way
so there's no doubt


rrrrun, rrrrrrrrun, children run or the retsnom eats'ya!!!!!
which waaaaaaay?
that waaaaaaaaaaaaaaaaaaaaay.
where's that waaaaaaaaaaaaaaaaaaaaaaaaaaaay?
CRUNCH...

 

[jsfisher]

Yes there are infinitely many distinct points (where a point is the smallest element) at any arbitrary scale level of Mandelbrot set, which stay distinct because among them there are always smaller elements, which are irreducible into points.

Mandelbrot set and Koch fractal are both based on the co-existence of smaller AND smallest.

As has already been pointed out, you are wrong. You assert out of ignorance.

Here is an example of the co-existence of smaller AND smallest at Koch fractal:

[qimg]http://farm3.static.flickr.com/2707/4408536446_ce60c7d35f_z.jpg?zz=1[/qimg]

I see you still cannot distinguish between the actual Koch snowflake and its generator.

 

[doronshadmi]

I see you still cannot distinguish between the actual Koch snowflake and its generator.

I see that you are unable to comprehend the actual existence of Koch fractal as a result of the co-existence of smaller AND smallest.

(Given every smaller element under the co-existence, it is not reducible to the smallest element) AND (Given every smallest element under the co-existence, it is not extendible to any smaller element).

The Man asked me

...Smaller than what?...

My answer is:

Smaller than all greater elements, which is also irreducible to the smallest element.

The minimal expression of smaller is a 1-dim element between any arbitrary closer smallest 0-dim elements, which saves their distinction w.r.t each other upon all arbitrary given scales, exactly because smaller element exists at-once in more than one 0-dim location (which is a property that no 0-dim element has).

The minimal expression of smallest is 0-dim element, which exists at one and only one location w.r.t the entire elements upon all arbitrary given scales.

However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms. ( http://en.wikipedia.org/wiki/Fractal )

The self similarity over scales that is based on the co-existence of smaller AND smallest, is resulted by a bijection between the points on all smaller or grater line segments, which is collapsed into a single point (the smallest, and therefore, no bijection) without the co-existence of (smaller OR greater) AND smallest.

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).

 

[doronshadmi]

If you could comprehend both generating formulas and their iteration, then you would see not only the difference between those two objects but most importantly you would see no traces of "Smaller" and "Smallest" -- the two barbarian tribes that try to invade the civilized math world. And that's the point. You said "if you zoom in . . ." but never did.

You are invited to define the complexity of Math by using only the smallest.

 

[doronshadmi]

Maybe it's because extension is the opposite to reduction, and during the process of extension things tend to be longer and not shorter, as it is happening in your "framework."

Smaller or Greater are the expression of the non-local under the co-existence with the local, where the local is the expression of the smallest.

 

[epix]

Smaller or Greater are the expression of the non-local under the co-existence with the local, where the local is the expression of the smallest.

And without doubt the lesser is blessed by the greater.
Hebrews 7:7

You two should get together.

 

[jsfisher]

I see that you are unable to comprehend the actual existence of Koch fractal as a result of the co-existence of smaller AND smallest.

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.

 

[The Man]

Unless both are considered.

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.

It is called difference. If there is nothing between A and B, the result is one and only one thing simply because "there is nothing between A and B" is equivalent to ""there is no difference between A and B".

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

The ridiculous and self-contradictory is the reflection of your only-context-dependent reasoning, when it is used to comprehend a reasoning that uses cross-contexts reasoning in addition to context-dependent reasoning.

Nope, again simply a result of you making reduiculous assertions that contradict just your ridiculous assertions.

You are lying to yourself by understand Collection only in terms of list.

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.

Your inability to understand the essential different ids of the smaller AND smallest under co-existence, is resulted by your misunderstanding of the concept of Collection
This is really some "profound" insight of you, The Man.

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 without the co-existence of smaller AND smallest.

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

The following definition …

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

mul•ti•plic•i•ty
   ˌmʌl təˈplɪs ɪ tiShow Spelled[muhl-tuh-plis-i-tee] Show IPA
–noun, plural -ties.
1.
a large number or variety: a multiplicity of errors.

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.

You are still missing the fact that non-locality and locality are understood as such only under their co-existence.

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.

Without this co-existence Multiplicity is impossible, and the observed complexity does not exist.

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 self-contradictory nonsense is entirely the result of the reflection of your only-context-dependent reasoning, when it is used to comprehend a reasoning that uses cross-contexts reasoning in addition to context-dependent reasoning.

Nope once again and as seen, above, it is just a result of you spouting nonsense that contradicts just your own nonsense.

 

[The Man]

My answer is:

Smaller than all greater elements, which is also irreducible to the smallest element.

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.

 

[epix]

The self similarity over scales that is based on the co-existence of smaller AND smallest, is resulted by a bijection between the points on all smaller or grater line segments, which is collapsed into a single point (the smallest, and therefore, no bijection) without the co-existence of (smaller OR greater) AND smallest.

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).

http://www.stsci.edu/~lbradley/seminar/

Doron, you shouldn't take the relation between fractals and chaos literally.