Deeper than primes

[Little 10 Toes]

Isn't that the same article that was not peer reviewed?

Edit: I also notice, your name isn't listed as an author. Funny since you're the one that "invented" the idea. Also, no mention in the abstract of OM.

 

[epix]

Slowly but surely OM notions are spread http://adsabs.harvard.edu/abs/2010AIPC.1232..299K .

Are OM notions spreading? If so, then the Harvard folks got a surprise when attempting to partition an integer where the number of elements is set finite, like 3, for example. Let's start . . .

7 = 0 + 0 + 7

But since the non-zero element of the partition is identical to the integer to be partitioned, which is also the definiens, a "regression" emerges:

7 = 0 + 0 + 0 + 0 +7

Now the partition has 5 elements, and the recurrence let the process of partitioning approach infinity.

You can use a general form and partition integer g this way:

g = {0 + 0 + g}

which is a form very similar to the troublesome

G = {A, A, G}

There surely must be some difference between '=' and '='.

 

[jsfisher]

The Man, I see that also jsfisher does not agree with you about the identity of a member of set A to set A.

And again, a lie!! Doron, where did I either agree--which you said I did--or disagree--which you said I did--with this statement you attribute to The Man?

Is it compulsive, Doron, that you have to fabricate things?

Most children learn the difference between telling the truth and lying before kindergarten. Did you forget, or do they just not teach anything about honesty where you are?

 

[doronshadmi]

Really? This would be the same Moshe Klein who you chased away when he tried to understand OM, but in fact showed that even you did not understand it?

Yes really.

This is the same Moshe Klein, which wrote an article together with Prof. Andrei Khrennikov and Prof. Tal Mor about sub-partitions, which is based on the strict case of Organic Numbers.

 

[doronshadmi]

Isn't that the same article that was not peer reviewed?

Edit: I also notice, your name isn't listed as an author. Funny since you're the one that "invented" the idea. Also, no mention in the abstract of OM.

Please register to http://scitation.aip.org/getabs/ser...0001000299000001&idtype=cvips&gifs=yes&ref=no , open the article and you will find my name together with Moshe’s name, which refers to http://www.scribd.com/doc/18453171/International-Journal-of-Pure-and-Applied-Mathematics-Volume-49 .

 

[doronshadmi]

Are OM notions spreading? If so, then the Harvard folks got a surprise when attempting to partition an integer where the number of elements is set finite, like 3, for example. Let's start . . .

7 = 0 + 0 + 7

But since the non-zero element of the partition is identical to the integer to be partitioned, which is also the definiens, a "regression" emerges:

7 = 0 + 0 + 0 + 0 +7

Now the partition has 5 elements, and the recurrence let the process of partitioning approach infinity.

You can use a general form and partition integer g this way:

g = {0 + 0 + g}

which is a form very similar to the troublesome

G = {A, A, G}

There surely must be some difference between '=' and '='.

Please register to http://scitation.aip.org/getabs/ser...0001000299000001&idtype=cvips&gifs=yes&ref=no in order to read its content, before you reply.

 

[doronshadmi]

And again, a lie!! Doron, where did I either agree--which you said I did--or disagree--which you said I did--with this statement you attribute to The Man?

Is it compulsive, Doron, that you have to fabricate things?

Most children learn the difference between telling the truth and lying before kindergarten. Did you forget, or do they just not teach anything about honesty where you are?

Evasion noted.

It must be stressed that in this case jsfisher has only two options:

1) A set is identical to its member.

2) A set is not identical to its member.

He chose Evasion.

 

[zooterkin]

Yes really.

This is the same Moshe Klein, which wrote an article together with Prof. Andrei Khrennikov and Prof. Tal Mor about sub-partitions, which is based on the strict case of Organic Numbers.

I find that hard to believe, since you've yet to provide an adequate description, let alone a strict definition, of what an Organic Number actually is.

 

[doronshadmi]

I find that hard to believe, since you've yet to provide an adequate description, let alone a strict definition, of what an Organic Number actually is.

http://www.internationalskeptics.com/forums/showpost.php?p=6329939&postcount=11525

 

[zooterkin]

http://www.internationalskeptics.com/forums/showpost.php?p=6329939&postcount=11525

A) Please learn to use the forum software properly to quote posts, rather than bare links.

B) That doesn't answer my point at all. Please give a clear definition (here, not a link to yet another PDF with pretty pictures) of what an Organic Number is, and what you can do with it.

 

[doronshadmi]

not a link to yet another PDF with pretty pictures

An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

X is a placeholder of a given element.

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:

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.

Edit:

http://www.internationalskeptics.com/forums/showpost.php?p=5837358&postcount=954

http://www.internationalskeptics.com/forums/showpost.php?p=5974148&postcount=9988

 

[zooterkin]

An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

X is a placeholder of a given element.

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:

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.

http://www.internationalskeptics.com/forums/showpost.php?p=5837358&postcount=954

You seem to have overlooked (although you did go to the trouble of snipping them) the key words in my request:

B) That doesn't answer my point at all. Please give a clear definition (here, not a link to yet another PDF with pretty pictures) of what an Organic Number is, and what you can do with it.

 

[doronshadmi]

You seem to have overlooked (although you did go to the trouble of snipping them) the key words in my request:

It is a clear definition that is based on clear Logic.

All you have to do is get out of your box, where in this box a line is made by points.

 

[The Man]

Any given member that is included in set A, is not identical to set A.

Again, it is when the member is specified to be that set.

The maneuvering with names like “subset” and “set” has no significance, because these names are actually the same object.

Doron, you’re the only one trying to ‘maneuver’ with names.

I see you’ve missed the point. Set A and A as a member of set A are not identical, because set A has an additional level that A as a member of set A does not have, ad infinitum ...

I see you’ve missed your own point about “maneuvering with names”, again.

In that case you get a set that is based on infinite regression, and infinite regression does not have strict identity. Again, any given set is identical to itself, also any given member is identical to itself, but no member of a given set is identical to that set.

Again this “infinite regression” is only in your imagination because you seem to have some sort of “identity” crisis about how you represent set “A”.

You still miss the difference between “define by” or “defined as” and “identical to”.

Nope, you still miss that your own failed reasoning is still only yours no matter how much you want to ascribe it to someone else.

The “strict” one (which asserts that a given member of a given set is identical to that set) is exactly the naive notion that leads to fantasies like Russell’s Paradox and proper classes.

Once again you clearly demonstrate that you have no idea what you are talking about.

Here is the non-truncated quote again.

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then
• A is also a proper (or strict) subset of B; this is written as
or equivalently
• B is a proper superset of A; this is written as

It is all derived from the fantasy that the magnetite of existence of infinite collected members is identical to the magnitude of existence of a given collector, which leads to the inability to distinguish between “define by” or “defined as” and “identical to”.

Once again stop simply trying to posit aspects of your own failed reasoning onto others.

Set is a collector\collected framework that enables the existence of collections, whether they are empty or not.

In this case the “collected” is the “collector”.

Evidently the notion of “Set is a collector\collected framework that enables the existence of collections, whether they are empty or not”, is simply beyond you.

Nope, just your usual dichotomistic nonsense.

The traditional one.

So you don’t know what that “traditional one” is or how to express it accurately?

And this fact prevents a member of that set to be identical to that set.

The fact that it is still just set “A” prevents it from not being, well, set “A”, so they are in fact identical by that fact.

A set is defined by its members, but it does not mean that any of these members is identical to that set.

Once again it does if that set is defined as one of its members.

The “crisis” is your fantasy that can’t distinguish between “Identical to” and “defined by” or defined as”.

Doron, I’m not the one claiming some “identity” changes just because you use a different representation that you still equate to your set “A”. The crisis and ignorance remains entirely yours.

Organic Mathematics has no “crisis” about the notion of the incompleteness of infinite collections.

Actually it does, since you simply don’t like “infinite collections” it leaves your OM extremely restricted.

On the contrary, the traditional notion has a “crisis” about this subject because it can’t distinguish between “Identical to” and “defined by” or defined as”.

Once again stop simply trying to posit aspects of your own failed reasoning onto others.

The traditional notion uses frameworks like ZF(C) in order to avoid paradoxes that do not exist, and it also using a garbage can called “proper classes”.

Doron you keep going on about the problems and paradoxes resulting from a set including itself as a member, so who are you trying to kid with this “do not exist” nonsense (other than just yourself)?

The fact that Set A is defined by these iterations, does not mean that any of these iterations is identical to set A.

Doron you equated them to set “A” yourself, so stop kidding yourself.

Once again stop simply trying to posit aspects of currently agreed failed reasoning onto others.

I have asserted and continue to assert that you don’t even agree with yourself, so don’t kid yourself about me trying to posit some or any ‘agreement’ upon you or anyone else.

The Man, I see that also jsfisher does not agree with you about the identity of a member of set A to set A.

How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.

 

[The Man]

Happy Birthday to you, The Man.

Thank you very much.

 

[The Man]

Doron can actually do this due to the definition of an element A of a set S: A is an element of S if and only if A is not an element of A.

Here is a tautology that deals with a similar situation:

y = 2x - 5y

y + 5y = 2x
6y = 2x
y = (2x)/6

If the tautology doesn't tolerate 'y' on both sides, then there could be a problem with A = {A, B, C}, as it was, coz Godel got busy with it.

As I said before…

Doron a letter does not define a set it is simply used to represent a set and you equate your letter (set “A”) to all your various instances of different “bracketed notation”, thus asserting them as, well, equal. All you have is set “A” so your “different levels of a given set” are all just set “A”. Your “infinite regression” is just in your imagination as there is nowhere for you to regress to, you only have set “A”. Sure, in this case, it is both the set and the element of that set, you can go around that circle as many times as you like but you just end up back were you started with only set “A”.

Since “(2x)/6” = “y”, technically ‘y’ is on both sides (more specifically both sides are equally representative of ‘y’). The technical name for this is ‘term rewriting’ (which we have been over with Doron before). You can represent ‘y’ or set “A” any number of different ways, but you are still simply representing ‘y’ or set “A” in either given case.

 

[jsfisher]

Evasion noted.

It must be stressed that in this case jsfisher has only two options:

1) A set is identical to its member.

2) A set is not identical to its member.

He chose Evasion.

Evasion? Of your misinterpretation of The Man's statement? --Not hardly.

The issue -- which you are evading -- is your continued out-right lying about what other people said or meant.

You are a proven dishonest person, Doron. You have destroyed your own credibility and your integrity. It sucks to be you.


By the way, the text quoted above is an example of a false dichotomy. Doron gets nothing right.

 

[doronshadmi]

Again, it is when the member is specified to be that set.

Right, exactly as True is specified to be False, see? I also know to use this kind of trick.

I see you’ve missed your own point about “maneuvering with names”, again.

Yes, by using the name "level" in The Man's flat-land.

Again this “infinite regression” is only in your imagination because you seem to have some sort of “identity” crisis about how you represent set “A”.

Crisis ?? no way, I like infinite regression of infinite levels after it is one of the possible ways to express Complexity.

The Crisis is a direct result of forcing completeness on such an expression, because in flat-land there can't be levels and as a result we get the illusion that a member of X is identical to X, which of course is resulted by fantasy illusion like Russell's paradox and garbage can like proper classes.

The Man, imagination is good, because it can help you to see beyond flat-land, illusion is bad because you keeps you locked under flat-land.

you still miss that your own failed reasoning

You still miss your own flat-land reasoning.

In this case the “collected” is the “collector”.

I know, this is a normal day in flat-land.

Nope, just your usual dichotomistic nonsense.

Another normal experience in flat-land, which naturally gets different levels as dichotomy.

The fact that it is still just set “A” prevents it from not being, well, set “A”, so they are in fact identical by that fact.

It is the best reasoning that you can get in flat-land, you are right.

Once again it does if that set is defined as one of its members.

Yes I know, also a line segment is identical to the end-points that define it, isn't it The Man from flat-land?

Actually it does, since you simply don’t like “infinite collections” it leaves your OM extremely restricted.

Ho, I truly like infinite collections exactly as they are, well, infinite.

Once again stop simply trying to posit aspects of your own failed reasoning onto others.

Once again stop simply trying to posit aspects of the currently agreed flat-land reasoning onto others.

Doron you keep going on about the problems and paradoxes resulting from a set including itself as a member, so who are you trying to kid with this “do not exist” nonsense (other than just yourself)?

The Man you keep going on about the problems and paradoxes that do not exist, because no member is identical to its set.

I have asserted and continue to assert that you don’t even agree with yourself

The assertions of a person that does not get the concept of different levels, do not hold water.

How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.

Simple True\False Logic:

Closed box reasoning has been noted.

Your agreed reasoning, which asserts that a member is identical to its set, does not hold water.

Where did I agree to that? You are lying again, Doron.

By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.

So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that you, The Man, are using.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.

 

[doronshadmi]

You are a proven dishonest person, Doron. You have destroyed your own credibility and your integrity. It sucks to be you.

It was shown time after time that your "you are lying" does not hold water, exactly as it does not hold water in your last "you are laying" case:

How about actually linking the quote, as it seems evident that he was simply not agreeing with your assertion that he agreed to something and I would agree with him. As you often simply assert nonsense claiming people agree with it.

Simple True\False Logic:

Closed box reasoning has been noted.

Your agreed reasoning, which asserts that a member is identical to its set, does not hold water.

Where did I agree to that? You are lying again, Doron.

By jsfisher's reply I am lying if I assert that jsfisher agrees that a member is identical to its set.

So since I am lying, then by True\False Logic jsfisher does not agree that a member is identical to its set, which is the assertion that The Man using.

Jsfisher clearly does not use here Ternary Logic, because he claims that I am lying.

 

[epix]

An Organic Number is a conceptual form that is derive from the linkage among Non-locality and Locality, which enables to deal with parallel (uncertain) and serial (certain) information under a one framework.

The logical reasoning of Non-locality and Locality is defined as follows:

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

The reasoning is not logical; it's a dogmatic and unsupported declaration.

Inclusion and exclusion compared as above: a nut N is inside the nut shell {} AND at the same time it is not. That's hard to believe, but seeing is believing:

N = {N}

What do you see, Bernie?

I see two nuts: one is outside the nutshell and the other is inside the nutshell.

You see wrong: there is only one nut: ONE is local to the shell {} and ONE is non-local to the shell.


Too bad that for the total lack of necessary awarness of your own ideas, you defined the result of Inclusion(True) and Exclusion(True) in such a sorrowful, dogmatic way.

Do PARrot and PARadox share the same etymology? PAR=PAR, afterall.