Deeper than primes

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Doron! Hey, what a surprise! Come on in . . .
Want something to drink? Goat milk? I'll get you some. Have a seat.


[qimg]http://a.imageshack.us/img339/5306/seat1h.jpg[/qimg]


OOOOOOOUCH!!!



:confused:



[qimg]http://a.imageshack.us/img710/3083/seat2r.jpg[/qimg]





[qimg]http://a.imageshack.us/img256/3920/seat3.jpg[/qimg]

Be aware of mischievous demon Ekklund.

Real complexity does not necessarily obey boxes.
 
The Greek text makes the word considerably shorter: Pi.

did you ask me who I am
in the wee hour of 3 am?
3 is round and starts odd primes
and I shall answer 14 times

I abhor your interference
for my real name is Circumference
3 is prime and also odd
on your knees, for I'm your god

:jaw-dropp

Great epix :)
 
How about some context Doron? That would be helpful if you’re replying to post from almost a year ago.
Do you actually state that you can't reply to my post because it was written a year ago?

In this case you agree that reasoning is time dependent, and can be changed by paradigm's shift.

Here is a paradim's shift:

The line part of the complex called segement, is not an aggregation of sub-segmenets or points.

A line (whether it is a part of a complex called segment, or an endless (edgeless) straight line) is the minimal representation of a non-local atom.

A point is the minimal representation of a local atom.

The logical foundation of the membership of these atoms is as follows:

Membership is the relation of X w.r.t Inclusion\Exclusion.

The non-local aspect of Membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are the same w.r.t Inclusion\Exclusion, then X Membership is called non-local w.r.t Inclusion\Exclusion.

The local aspect of membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are different w.r.t Inclusion\Exclusion, then X Membership is called local w.r.t Inclusion\Exclusion.


Here is a 2-valued view of these definitions:

Code:
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

NOR+AND ---> NXOR so we are dealing here with NXOR\XOR Logic, where both Non-local and Local Memberships are logically defined.

The Man, please support your claim in http://www.internationalskeptics.com/forums/showpost.php?p=5429765&postcount=7600.
 
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Here is a 2-valued view of these definitions:

Code:
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

It could have gone this way:

[] = absence

[.] = presence

[ ]. = local (an influence of the dot on the bracket; can open the door: from [] to [ ])

[] . = not local (no influence of the dot on the bracket ; cannot open the door)

It didn't.
 
It could have gone this way:

[] = absence

[.] = presence

[ ]. = local (an influence of the dot on the bracket; can open the door: from [] to [ ])

[] . = not local (no influence of the dot on the bracket ; cannot open the door)

It didn't.

No, Non-locality means that X has an influence even if it is not only-Included or only-Excluded w.r.t Inclusion\Exclusion.
 
In examples 1,2,3 below we can see that there is more than a one closed version that is based on finite cardinalities 2,3,4, … etc... along a given 1-d path:

4297878664_d74c38b77e_o.jpg


By following this observation, let us improve our game in http://www.internationalskeptics.com/forums/showpost.php?p=6292968&postcount=11405.

The improved game is called "Return to the first".

It is played along a 1-d path.

1) The players are points, such that each point (accept an arbitrary first chosen point) is visited only once.

2) The game is completed if the arbitrary first chosen point is visited twice.

By following the rules of this game, it is completed if there is a finite amount of players along the 1-d path.

By following the rules of this game, please provide a proof that the game is completed also if there is an infinite amount of players along the 1-d path.
 
By following http://www.internationalskeptics.com/forums/showpost.php?p=6296841&postcount=11439 Russell's paradox is a fantasy because given S() , which is the set of all sets that are not one of their members , S() is one of that sets only it is not one of its members.

The calm the if S() is one of that sets, then it must be one of its members, is a false claim, which is based on the misunderstanding of the difference between a given set and a given member of that set.

A(…),B(…),C(…) etc… are sets that are not one of their members.

So S( A(…), B(…), C(…), …) is the set of all sets that are not one of their members, only if it is not one of its members.
 
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The men, you have missed

Nope, in fact I quoted you. However, you seem to deliberately miss the 'not' in one of your examples.

Look:



No, "necessarily different" and ~"necessarily different" are "necessarily different".


No, "necessarily different" and -"necessarily different" are ~"necessarily different".

Nope, “~"necessarily different"” and “-"necessarily different"” are necessarily different from, well, "necessarily different" again it is the addition of the symbols representing 'NOT' that are the give away.


No, “everything but” holds only in the case of finite amount, where “anything but” holds in both finite and infinite amounts. Play the game at http://www.internationalskeptics.com/forums/showpost.php?p=6292968&postcount=11405 to get this notion.

Again, your assertion, your problem, it restricts no one but you.


Your “game” still fails you, as it did over a year ago.






No, it is a built-in property, for example:

Then it is not an “extension” but simply a “built-in property”, by your own assertion.

The existence of the concept of Set extends the existence of members, and this notion is notated by the outer "{""}", whether a given set is empty or not.

Again “extends” how and to where? “extends the existence of members”? Do these extended members exist longer with your “extension” than without?


You sure you didn’t get this extended member idea from a ‘smiling Bob’ commercial?

How does the “concept of Set” ‘extend’ “the existence of members” for a set where no members, well, exist as you claim?



Do you understand that D() does not require 0(), 1(), 3() ... etc., exactly as {} does not require members?

You don’t understand that your nonsensical “notations” only represent you extending your nonsense.





Russell's paradox is a direct result of the misunderstanding of the difference between a given concept and the members of that concept (see http://www.internationalskeptics.com/forums/showpost.php?p=6293098&postcount=11410).

Nope, once again it is specifically about a set being a member of it self.


For example, the existence of the concept of Ideas I() extends the existence of any member of this concept, including I(I()).

Again “extends” how and to where?


So the member of I(I()) is not identical to the concept of Ideas I().


Unless it is a member of itself as in Russell's paradox.


By this real non-naïve understanding of the concept of Set, There is no such a thing like a member of given set, which is identical to that set.

What “concept of Set” are you referring to?


The Man, your reasoning does not hold water, and in the case of the concept of Dimension it can't be used to distinguish
between the absence of D(), and 0().

Again what “concept of Dimension” are you referring to? They are your nonsense notions Doron, distinguishing between them or their absence is evidently of interest only to you.



Do you actually state that you can't reply to my post because it was written a year ago?

Do you actually state that your post was written a year ago and not simply what you quoted from my post that was written a year ago?

Do you actually state that you can't tell that…


How about some context Doron? That would be helpful if you’re replying to post from almost a year ago.

…was a reply to your post three days ago where you quoted something from a almost a year ago?

In this case you agree that reasoning is time dependent, and can be changed by paradigm's shift.

I don’t think anyone here (other then you) has argued that our understanding can not and does not change.

Here is a paradim's shift:

Indeed, a shift into meaningless drivel.


The line part of the complex called segement, is not an aggregation of sub-segmenets or points.

Again your assertion, your restriction.

A line (whether it is a part of a complex called segment, or an endless (edgeless) straight line) is the minimal representation of a non-local atom.

A point is the minimal representation of a local atom.

Again your meaningless ascriptions.

The logical foundation of the membership of these atoms is as follows:

Membership is the relation of X w.r.t Inclusion\Exclusion.

The non-local aspect of Membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are the same w.r.t Inclusion\Exclusion, then X Membership is called non-local w.r.t Inclusion\Exclusion.

The local aspect of membership w.r.t Inclusion\Exclusion, is defined as follows:

If the truth values of X are different w.r.t Inclusion\Exclusion, then X Membership is called local w.r.t Inclusion\Exclusion.


Here is a 2-valued view of these definitions:

Code:
Inclusion\Exclusion 
  F            F          [ ]    (Non-locality)  (NOR)

  T            F          [.]    (Locality)--|
                                             |-- (XOR) 
  F            T          [ ].   (Locality)--|

  T            T          [[u] ][/u]_   (Non-locality)  (AND)

NOR+AND ---> NXOR so we are dealing here with NXOR\XOR Logic, where both Non-local and Local Memberships are logically defined.

Again your self –contradictory “logic”.



Certainly, I did not miss the posts you thought I did, thus your thinking that I did was incorrect.




I suggest that you look at it.
 
No, Non-locality means that X has an influence even if it is not only-Included or only-Excluded w.r.t Inclusion\Exclusion.
Not in other disciplines where the helper descriptive term is used. An object is said to be local to a certain environment and is assumed to exert influence or be influenced by other objects that the object shares the environment with. In computer science where the term is also used, local objects have a function that expires when they leave a particular environment. In both cases the concept of the local/not-local (global) declaration of objects is very easy to understand, otherwise it would defy the purpose, which is an easier orientation. BUT . . . ! In some semi-spherical spaces, local objects can be declared nearly a random way.
 
Not in other disciplines where the helper descriptive term is used. An object is said to be local to a certain environment and is assumed to exert influence or be influenced by other objects that the object shares the environment with. In computer science where the term is also used, local objects have a function that expires when they leave a particular environment. In both cases the concept of the local/not-local (global) declaration of objects is very easy to understand, otherwise it would defy the purpose, which is an easier orientation. BUT . . . ! In some semi-spherical spaces, local objects can be declared nearly a random way.

Don't confuse Doron with facts. It is counter productive to his work.
 
The Man said:
How does the “concept of Set” ‘extend’ “the existence of members” for a set where no members, well, exist as you claim?
The notion of the extended existence of the concept of Set w.r.t. the existence of given members is notated by the outer “{“”}”, whether the set is empty or not, and this extended existence is a universal property of any given set w.r.t given members.

By understanding this universality, the set of (for example) all Ideas I() extends I(I(...), ...) such that no given member is identical to the given Set I().

The set of all oranges O() does not have member O(O(...), ...) and we get O(...), but it does not change the fact that no given member is identical to a given Set, because of the extended existence of any given set w.r.t any given member.

As for Russell’s Paradox, S() is the set of all sets that are not of the form X(X()), But since no member of S(), including S(S()), is identical to S(), then S(X(…), …) or S(X(…), …, S()) are both S().
 
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The Man said:
Nope, “~"necessarily different"” and “-"necessarily different"” are necessarily different from, well, "necessarily different
Nope, for example: ”~0” is "necessarily different than 0” where “-0” is ~"necessarily different than 0”.
 
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The Man said:
Again your assertion, your restriction.
In other words, you actually claim that your assertions are non-local w.r.t my assertions (which are isolated and non-acceptable) , and you take it as privilege of your reasoning.

Thank you for supporting my assertion about Non-locality.
 
there is an essential difference between "defined by" and "identical to".

Fore example:

The empty set is defined by emptiness but it is not identical to emptiness, otherwise we have emptiness (nothing) to deal with.

So the essential property of a set is the non-identity with its members.

This non-identity is expressed as the extension of the magnitude of the existence of a set with respect to any magnitude of existence of any possible member.

This essential difference between set and member of a set, naturally prevents Russell's Paradox, because no member of a given set is identical to that set.

The standard notion of sets is based on the notion that a member of a given set is identical to that set, and as a result, there is no difference between a set and its members, this indistinguishably is the core of the "defined by" notion among the concept of Set and the concept of Member, which naturally leads to paradoxes like Russell's Paradox.
 
The notion of the extended existence of the concept of Set w.r.t. the existence of given members is notated by the outer “{“”}”, whether the set is empty or not, and this extended existence is a universal property of any given set w.r.t given members.

By understanding this universality, the set of (for example) all Ideas I() extends I(I(...), ...) such that no given member is identical to the given Set I().

The set of all oranges O() does not have member O(O(...), ...) and we get O(...), but it does not change the fact that no given member is identical to a given Set, because of the extended existence of any given set w.r.t any given member.

As for Russell’s Paradox, S() is the set of all sets that are not of the form X(X()), But since no member of S(), including S(S()), is identical to S(), then S(X(…), …) or S(X(…), …, S()) are both S().

So just more of your extended nonsense notations.

Doron the set of all oranges does not have itself as a member because the set of all oranges is not, well, an orange. However the set of all sets would have both itself and the set of all oranges as members, which is why it is not considered a proper set. We have been over all this before. If you need some review I suggest you reread some of those old posts and the reference links provided.
 
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