Deeper than primes

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doronshadmi said:
You still do not get that a collection (no matter what principle is used to gather it) of infinitely many elements is a complex result of actually finite (can be represented as a point) and actual infinity (can be represented as an endless straight line) cannot be actual infinity. Since no complex can be actual, then any given infinite collection is incomplete w.r.t actual infinity (we have infinite extrapolation of distinct elements, in the case of N elements, and infinite interpolation in the case of Q or R elements).
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You still do not get that a collection is not “gathered” it is defined. This attributing of some kind of physical activity like gathering to a purely abstract activity like defining a collection, seem to be your major misconception. Incomplete means that it would be missing something that would have made it complete. As you assert your complex is comprised of your “actual infinity” and your “actually finite” your complex is complete in regard to your “actual infinity” as it does and must, by your own assertions, include your “actual infinity”. Anyway, once again claiming your complex is “actually finite” as well as “actual infinity” is just self-contradictory.

Again what exactly is “infinite” about your “endless atomic straight line”?
 
The Man said:
You still do not get that a collection is not “gathered” it is defined.
This attributing of some kind of physical activity like gathering to a purely abstract activity like defining a collection, seem to be your major misconception.
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Call it whatever you like, it does not change the fact that there is a principle
that determines what elements have certain properties, and this principle does not determine if these elements are considered as a complete collection of distinct elements. There is no limitation hare to physical elements, because all we care is that we deal with a collection of distinct elements (abstract or not) that have some common properties.
The Man said:
Incomplete means that it would be missing something that would have made it complete.
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Incomplete means that something is not an atom.
The Man said:
As you assert your complex is comprised of your “actual infinity” and your “actually finite” your complex is complete in regard to your “actual infinity” as it does and must, by your own assertions, include your “actual infinity”. Anyway, once again claiming your complex is “actually finite” as well as “actual infinity” is just self-contradictory.
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The term “all” w.r.t finitely many elements, does not mean that a complex of finite elements is complete. It simply asserts that each element of a certain universe is reachable and as a result, anything but that complex =().

This is not the case with a non-finite complex.

The Man said:
Again what exactly is “infinite” about your “endless atomic straight line”?
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It is an atom that its length is ∞.
 
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The Man said:
Then how do you define length?
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More accurately: “How I define a length of a complex?”

Very simple, by define a complex that is a non-local atom between two local atoms.

Now all we have to do is to call to this complex 1, and the rest of the complexities is defined w.r.t 1.

But it does not mean that we forget what enables complex 1, in the first place.

EDIT: Since we do not forget what enables complex 1, we immediately understand that no complex can be an atom, where an atom has at least two versions, which are: 0-length atom, ∞-length atom.
 
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doronshadmi said:
Call it whatever you like, it does not change the fact that there is a principle
that determines what elements have certain properties, and this principle does not determine if these elements are considered as a complete collection of distinct elements. There is no limitation hare to physical elements, because all we care is that we deal with a collection of distinct elements (abstract or not) that have some common properties.
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Doron “gathering” is a physical activity. Call it whatever you like but the principle that defines the particular elements of a set is the definition of that set and specifically the definition of what does or dose not constitute and element of that set.

doronshadmi said:
Incomplete means that something is not an atom.
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No it does not.

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

in⋅com⋅plete
–adjective
1. not complete; lacking some part.


2. Football. (of a forward pass) not completed; not caught by a receiver.


3. Engineering. noting a truss the panel points of which are not entirely connected so as to form a system of triangles. Compare complete (def. 8), redundant (def. 5c).


4. Logic, Philosophy.
a. (of an expression or symbol) meaningful only in a specific context.
b. (of a set of axioms) such that there is at least one true proposition (able to be formulated in terms of the basic ideas of a given system) that is not deducible from the set. Compare complete (def. 7).
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Simply making up your own ridiculous usages of words is one of the continuing problems your have is simply relating your notions and also a major source of confusion, misinterpretation as well as misrepresentation for you about standard application.

doronshadmi said:
The term “all” w.r.t finitely many elements, does not mean that a complex of finite elements is complete. It simply asserts that each element is a certain universe is reachable and as a result, anything but that complex =().
This is not the case with a non-finite complex.
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Nonsensical gibberish, that all defined elements of the set are elements of the set makes it complete.

doronshadmi said:
It is an atom that its length is ∞.
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Again how do you define length?
 
Little 10 Toes said:
A = ~B = B
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Since you have not provided evidence/proof that my equation is wrong based on your thinking, I will assume that your thinking is broken.

What other things that you believe in are wrong too?


Little 10 Toes said:
It's not a game. I am using your rules under your OM to show that your rules are broken. Please show where I am wrong. If this is nonsence, then it is because of your terms, your rules, and your OM.
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Even if it isn't based in OM, you are still using standard math terms in your own unique wrong way. Start using the terms correctly and review your ideas. Then come back and share.
 
doronshadmi said:
More accurately: “How I define a length of a complex?”
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No that would be less accurate in reference to your “endless atomic straight line” that you claimed had length. Are you now claiming that your “endless atomic straight line” does not have length since it is not “a complex”?

doronshadmi said:
Very simple, by define a complex that is a non-local atom between two local atoms.

Now all we have to do is to call to this complex 1, and the rest of the complexities is defined w.r.t 1.

But it does not mean that we forget what enables complex 1, in the first place.
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So your definition of length requires two of your “local atoms” also referred to by you as “ends”. As your “endless atomic straight line” has none it can not meet your definition of having any length.
 
The Man said:
No that would be less accurate in reference to your “endless atomic straight line” that you claimed had length. Are you now claiming that your “endless atomic straight line” does not have length since it is not “a complex”?



So your definition of length requires two of your “local atoms” also referred to by you as “ends”. As your “endless atomic straight line” has none it can not meet your definition of having any length.
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∞ is the length of a non-local atom.

0 is the length of a local atom.

Any other length referes to a complex such that 0 < length of a complex < ∞
 
The Man said:
Simply making up your own ridiculous usages of words is one of the continuing problems your have is simply relating your notions and also a major source of confusion, misinterpretation as well as misrepresentation for you about standard application.
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The major problem is exactly your refuse to get words from non-standard view.
 
by the way complex with length 1 can be also a circle, which is a non-local atom that is related w.r.t a single point (a single local atom).
 
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doronshadmi said:
The major problem is exactly your refuse to get words from non-standard view.
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Doron, you simply making up your own nonsocial usages of words and concepts is exactly why you misinterpret and misrepresent standard applications. It is incumbent on no one to “get” your misinterpretations and misrepresentations of standard applications. However it is incumbent upon you to actually understand those standard applications and usages in order for you to make any meaningful assertions about them.


ETA:
So your claim now is that infinite collections are incomplete simply because you are misusing the word complete. How surprising.
 
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doronshadmi said:
My definition of Length is not limited to collections of elements.
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Who said anything about the length (?) of a collection of elements?

doronshadmi said:
The "self-contradictory" is a direct result of your inability to get things beyond the concept of collection.
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Are you just replying to some voices in your head? Try actually addressing what was written as opposed to what you would have preferred had been written or whatever your made up non-standard meanings induce you to just make up about what was written.
 
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The Man said:
However it is incumbent upon you to actually understand those standard applications and usages in order for you to make any meaningful assertions about them.
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This is exactly what I did. I have found that the standard understanding of Completeness is wrong exactly because, Complexity is not understood (the atomic building-blocks that enable Complexity, are ignored).
 
doronshadmi said:
You, by defininig Lengh as a sum of elements.
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Where did I define length as a "sum of elements"? The assertion that finite lengths can be added to each other ad infinitum is not a definition of length, but the definition of infinity in terms of length. However I would not expect you to actually understand that.

You on the other hand have given your definition of length as requiring at least two points (your “local atoms” or “ends“) which could be considered as requiring a collection of those two points. Later you asserted…



doronshadmi said:
My definition of Length is not limited to collections of elements.
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In your usual self contradictory fashion simply proclaiming that your definition of length is not limited to your definition of length that you provided.

Still waiting for your actual definition of length that you use to determine an infinite length (as you claim) for your “endless atomic straightline”


ETA:

Just to try and make it easier for you, since you so enjoy combining two concepts into your complexes. An infinite length should generally combine the concept (or definition) of length with the concept (or definition) of infinity.
 
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doronshadmi said:
This is exactly what I did. I have found that the standard understanding of Completeness is wrong exactly because, Complexity is not understood (the atomic building-blocks that enable Complexity, are ignored).
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Doron, the fact that you have to redefine a term demonstrates that “the standard understanding of Completeness” was not wrong otherwise you would not have need to change the meaning of the word to simply conform with your “understanding of Completeness”. By the way “Complexity” is another word you have simply applied your own meaning to. So does it really surprise anyone that you are going to get a wrong “understanding of Completeness” based on your wrong understanding of “Complexity” resulting from your self-contradictory “atomic building-blocks that enable Complexity”?
 
doronshadmi said:
by the way complex with length 1 can be also a circle, which is a non-local atom that is related w.r.t a single point (a single local atom).
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Doron as explained to you some time last year, in order to define a rotation in terms of length you need a radius for the circle. Otherwise it is just 360 degrees, 2p radian or one rotation and that is not any specific length or circle (not even a unit circle) as it applies to any circumference of any circle. The radius is defined by two points, the center point and a point along the circumference. Please describe how you define a circle "with length 1" by just a single point as you just claimed you could.
 
doronshadmi said:
According to my theory prime numbers have less entropy than non-prime numbers, if less entropy means that there are less full multisets w.r.t a given whole number.
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The way I understood the issue was that when entropy refers to a degree of uncertainty, then you presented it in three cases: yes, no and maybe. So if you leave three identical cards on the table organized in line, such as AAA and come back later, you won't be able to tell whether someone reorganized the cards; in this case the degree of entropy is the highest and equals 1. As an opposite, if you arrange the cards as ABC and later you see ACB or BAC, you can tell that a single swapping took place while you were gone. In this case the degree of entropy is zero -- you are 100% positive that someone reorganized the cards. The third, the "maybe" case, involves AAB. If someone swaps first two cards, you won't be able to tell that the swapping took place. But if someone swaps the last two cards, which are not identical, you can tell that it was so. In this particular case, the degree of entropy is 0.5 of someone making a single swap. Instead of cards, you used addends of partitioned numbers, such as

yes: [1 + 2 + 3] = 6
maybe: [1 + 1 + 4] = 6
no: [2 + 2 + 2] = 6

with all possible ways to partition positive integers from 2 up. It follows that zero (yes) entropy involves partitions where all addends are distinct. That means, the way I understand it, you proposed that prime numbers -- when partitioned -- should comprise more subsets made of distinct addends. As I see it, the brute computer power is the judge to decide whether your proposition holds true or not, coz I'm very skeptical of any analytic proof, given the nature of the problem.
 
The Man said:
The assertion that finite lengths can be added to each other ad infinitum is not a definition of length, but the definition of infinity in terms of length.
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No collection of elements is actual infinity ∞ , and I would not expect you to actually understand that.

The rest of your posts is based on the inability to get the notion of actual infinity as a non-local atom.

The Man said:
You on the other hand have given your definition of length as requiring at least two points
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The Man said:
In your usual self contradictory fashion
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Can't get Length not in terms of a complex, isn't it The Man?

Blame your inability to get 0 or ∞ Length.

The Man said:
An infinite length should generally combine the concept (or definition) of length with the concept (or definition) of infinity
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∞ Length is some possible representation of actual infinity.

Another possible representation is NXOR connective.

Again, the notion of actual infinity is important and not any particular representation of it.
 
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The Man said:
Doron, the fact that you have to redefine a term demonstrates that “the standard understanding of Completeness” was not wrong otherwise you would not have need to change the meaning of the word
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"Nice" notion that actually says:

"Do not provide any other notion to a given word and use only the already agreed one".


How dogmatic.
 
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The Man said:
Doron as explained to you some time last year, in order to define a rotation in terms of length you need a radius for the circle. Otherwise it is just 360 degrees, 2p radian or one rotation and that is not any specific length or circle (not even a unit circle) as it applies to any circumference of any circle. The radius is defined by two points, the center point and a point along the circumference. Please describe how you define a circle "with length 1" by just a single point as you just claimed you could.
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You did not get it.

It can be any closed line which its circumference = 1.
 
epix said:
Instead of cards, you used addends of partitioned numbers
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The general concept is Distinction, no matter of how it is represented.

If we look only on the level of partitions of some whole number, then a prime number has less entropy then a non-prime number.

Since prime numbers are fundamental of Number Theory, I think that using them in order to measure Entropy (by using partitions) can open some door to an interesting research on this subject.
 
doronshadmi said:
Your equation is wrong and not based on my thinking.
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You still haven't shown any proof that I am wrong.

Sorry that you feel that my equation of A = B = ~B is wrong. Show me where it is wrong. This equation is based on your definition that ~(something) is "anything but something". Your definition had to come from somewhere. You must have thought of it. Your words are based off of your thinking. For example:

If the universe is [A, B, C, D] then:

~(=A) --> =B OR =C OR =D
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Your definition from this message http://www.internationalskeptics.com/forums/showpost.php?p=5410062&postcount=7481

and
Anyone can write ~~~~~~A iinstead of =A, so?
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is from http://www.internationalskeptics.com/forums/showpost.php?p=5419139&postcount=7514

If you cannot show exactly where my thinking is wrong, I must be right. I have shown the proof that confirms my equation is correct. You say I am wrong, but you have not shown any proof. Show me some.
 
jsfisher said:
And just to close the loop for epix, why not tell him what you mean by this term, distinction, you throw about so casually.
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Both parallel (superposition of ids) and serial (strict ids) under a one comprehensive framwork.
 
Little 10 Toes said:
Hey doronshadmi. I notice that The Man called you out for claiming that he was "defininig Lengh [sic] as a sum of elements." Either retract your statement or show where he said that.
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For The Man a Lengh is the sum of elements in a given interval exactly because he rejects non-local atom.
 
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doronshadmi said:
No collection of elements is actual infinity ∞ , and I would not expect you to actually understand that.

The rest of your posts is based on the inability to get the notion of actual infinity as a non-local atom.





Can't get Length not in terms of a complex, isn't it The Man?

Blame your inability to get 0 or ∞ Length.


∞ Length is some possible representation of actual infinity.

Another possible representation is NXOR connective.

Again, the notion of actual infinity is important and not any particular representation of it.
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I never asked about length “in terms of a complex” and by your own assertions above your “length” “in terms of a complex” is not applicable to the length of your “endless atomic straightline”. Since even an infinite collection of your lengths “in terms of a complex” can not possibly represent your “actual infinity” length of your “endless atomic straightline”.

Blame your inability to make at least self-consistent and non-contradictory assertions.

So I’m still waiting for your definition of length that actually applies to you “endless atomic straightline”, like I asked, and not some definition of your “complex” length that you specifically claim can not possibly represent the ‘actual infinite’ length of your “endless atomic straightline”. Again you may effectively fool yourself with such shenanigans, but I doubt they will fool anyone else.
 
doronshadmi said:
"Nice" notion that actually says:

"Do not provide any other notion to a given word and use only the already agreed one".


How dogmatic.
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Doron you already have words to express what you mean "not an atom".

doronshadmi said:
Incomplete means that something is not an atom.
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Thus the only reason for you to make up some contrived new meaning for the word “incomplete” is to simply confuse yourself or others.

There is nothing “dogmatic” about standard or common usage (which is all the definition of a word is). If a usage becomes common it is a common usage.


Just because an “atom” (meaning singular and indivisible) is by that very nature complete does not infer that anything “not an atom” (not singular and is divisible) must then be incomplete. Just because something has the possibility to be incomplete does not require that it be incomplete.

In fact your usage is just inconsistent with your own notions (how surprising is that?). If incomplete means “not an atom” then any of your complexes or collections is “incomplete” including finite collections or complexes and that would just be inconsistent with the word finite.

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

fi⋅nite
–adjective

2. Mathematics.
a. (of a set of elements) capable of being completely counted.
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Is it your intention to attempt to redefine every word and concept in mathematics into some self-inconsistent and self –contradictory mess such that no one can understand math any better than you do? That certainly seems to be your modus operandi.
 
doronshadmi said:
You did not get it.

It can be any closed line which its circumference = 1.
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You do not get it, a “circumference = 1” requires a radius of 1/2p and a radius requires at least two points, the center point and a point on the circumference. So you just like to claim that…

doronshadmi said:
by the way complex with length 1 can be also a circle, which is a non-local atom that is related w.r.t a single point (a single local atom).
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Because you are simply ignoring that a circle (especially where ““circumference = 1”) is defined by its radius, requiring at least two points? How surprising.

Again, please, be my guest and actually define length using “any closed line” and referencing only one point, as you have now claimed you can.
 
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