Deeper than primes

[Little 10 Toes]

No, Independent Membership is a novel notion that holds between atoms, where atoms are existing AND empty things.

The result of the Independent Membership is a complex, where a complex is (Atom-A AND atom-B), such that the Atom-B property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-A, and Atom-A property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-B.

You will not find this novel notion in wikipedia, because wikipedia deals with already agreed things.

Do not try to find the key in order to get OM under the already agreed street light.

In order to get OM you have to go beyond the already agreed, and this is the essence of a paradigm-shift, which in this case is inevitable.

The Man and jsfisher and The Man do not make the inevitable step to OM, and as a result they are not there and stay closed under the current paradigm, which is too weak in order to get OM’s reasoning.

Their failure to get OM is spread all along this thread.

Perhaps you missed the point of the post. Since you claim n and k are atoms (things that are not sets) then n can not be part of k and k can not be part of n. Because of that, the rest of your reasoning is faulty.

 

[jsfisher]

No idea, but it really doesn't matter. Whether he's a fisherman or a Ph.D., if his theory is correct, then it will be accepted by professional mathematicians. I really see no reason for him to be here, since he's obviously not convincing anyone.

Why do you assume there are no professional mathematicians here?

 

[ddt]

What qualifications does Doron have?

He claims in the days of yore to have solved a bug in some program his employer used. After that, he became a programmer himself. Now he is CAD manager. I shudder to think of the quality of his programs. But the one bug he solved before being a programmer spurned him to become the Saviour of mathematics.

ETA: this from memory from what Doron told in previous threads.

No idea, but it really doesn't matter. Whether he's a fisherman or a Ph.D., if his theory is correct, then it will be accepted by professional mathematicians. I really see no reason for him to be here, since he's obviously not convincing anyone.

What jsfisher said - the same accounts for various other fora he has posted on. BTW, should I repost that list I once made of all the fora he has been posting on? Though it's not unheard of that fishermen turn mathematician, it's more common they start a church. Just putting the R in this R&P-thread.

 

[doronshadmi]

Perhaps you missed the point of the post. Since you claim n and k are atoms (things that are not sets) then n can not be part of k and k can not be part of n. Because of that, the rest of your reasoning is faulty.

n =1 to ∞

K = 0 to n-1


n or k are not parts of each other.

(n AND k) is a complex that is based in building-block n and building-block k, such that n or k are not building-blocks of each other.

You still closed under wiki and do not get the novel notion of Independent Membership, where atoms belongs to each other by their common property (which is the absence of building-blocks) but they are also independent of each other such that k belongs XOR does belong to n (it is local w.r.t n) and n belongs AND does not belong to k (it is non-local w.r.t k).

Independent Membership between atoms (building-blocks) is a novel extension of the concept of ur-element (the old paradigm of ur-element, as appears in wiki, is based on comparison with Ddependent Membership, where n is a collection that depends on k elements for its definition , where by the old paradigm of ur-elements, a ur-element is some k of n, that is not used as n to k elements).

In other words, you still do not get the novel notion of Independent Membership between k and n such that (n AND k) is not k-only or n-only.

This is exactly the reason of why the k property of (n AND k) prevents from (n AND k) to be n-only (and as a result we have infinite extrapolation between (n AND k) and n-only.

Also this is exactly the reason of why the n property of (n AND k) prevents from (n AND k) to be k-only (and as a result we have infinite interpolation between (n AND k) and k-only.

More particular:

Since a line segment is a complex (1-D AND 0-D) then no amount of complex (1-D AND 0-D) is 1-D (and we have infinite extrapolation between complex (1-D AND 0-D) and 1-D).

Also no amount of complex (1-D AND 0-D) is 0-D (and we have infinite interpolation between complex (1-D AND 0-D) and 0-D).

Standard Math, which is based only on local reasoning of the concept of Membership (where k belongs XOR does not belong to n (which is Dependent Membership), is too weak in order to deal with Independent Membership between atom k and atom n.

 

[doronshadmi]

Ok, so non-local is based on belong, and belong is based on membership. However, since it is membership between atoms, this is not the normal set membership. So, Doron, all you have done is jumped from one term to the next without defining anything. Well done!

Unfortunately, that leaves your terms as still meaning nothing. Is that really what you wanted? Is it really all that hard to given some semblance of meaning to any of your words?

Thank you for ignoring the difference between Dependent Membership (the standard one) and Independent Membership (the novel one).

http://www.internationalskeptics.com/forums/showpost.php?p=5295392&postcount=6724 can help.

 

[zooterkin]

n =1 to ∞

K = 0 to n-1


n or k are not parts of each other.

What sort of atoms are n and k?

 

[doronshadmi]

Doron, just how do you figure this excerpt relates to anything recently posted in this thread? I wager you can't even explain the significance of R_q(q).

The Man claims that y is true because it is an axiom of framework X.

If it was the case, then y cannot be undecidable within axiomatic system X.

The only alternative is that y is a true theorem of X that is undecidable within axiomatic system X.

As a result we get an infinite extrapolation of X, such that y is undecidable by an infinite extrapolation of X.

In other words, y belongs (it is a true theorem of X) AND does not belong to X (undecidable by an infinite extrapolation of X, or in other words, it is permanently beyond deductive systems of X extensions, and the non-locality of y theorem is clearly shown w.r.t deductive systems of X extensions).

Strong deductive axiomatic systems (systems that are strong enough to deal with Arithmetic) must be consistent AND incomplete, according to Gödel’s incompleteness theorems, and the simplest solution for this result is the acceptance of Non-locality as a fundamental property of the mathematical science, in addition to its Local property.

This novel solution is seen in http://www.internationalskeptics.com/forums/showpost.php?p=5289082&postcount=6704.

 

[doronshadmi]

No idea, but it really doesn't matter. Whether he's a fisherman or a Ph.D., if his theory is correct, then it will be accepted by professional mathematicians. I really see no reason for him to be here, since he's obviously not convincing anyone.

1) I am here for one and only one reason, which is: to develop my ideas, and I must say that it works.

2) I am fully aware of the fact that there is a Zero chance that my ideas will be accepted by the current community of professional mathematicians, for a good reason from their point of view, because if my ideas are accepted then fundamental body of knowledge, used today by “pure mathematicians” is changed by a paradigm-shift.

 

[jsfisher]

Thank you for ignoring the difference between Dependent Membership (the standard one) and Independent Membership (the novel one).

Are these part of your fall line of fashionable terms you refuse to define?

 

[jsfisher]

The Man claims that y is true because it is an axiom of framework X.

Oh, yeah? Just where did he do that?

If it was the case, then y cannot be undecidable within axiomatic system X.

The only alternative is that y is a true theorem of X that is undecidable within axiomatic system X.

Or a "false theorem" that is undecidable, or a "false theorem" than is decidable, or ....

...more gibberish...

And none of that addressed my post. Here it is again. Please try to focus this time:

Doron, just how do you figure this excerpt relates to anything recently posted in this thread? I wager you can't even explain the significance of R_q(q).

 

[dafydd]

1) I am here for one and only one reason, which is: to develop my ideas, and I must say that it works.

2) I am fully aware of the fact that there is a Zero chance that my ideas will be accepted by the current community of professional mathematicians, for a good reason from their point of view, because if my ideas are accepted then fundamental body of knowledge, used today by “pure mathematicians” is changed by a paradigm-shift.

I thought that the Messiah Complex only applied to religion.

 

[jsfisher]

...because if my ideas are accepted then fundamental body of knowledge, used today by “pure mathematicians” is changed by a paradigm-shift.

It would be more of a clumsy stumble, followed by face against pavement, followed by a loud "Doh!!"

 

[Little 10 Toes]

n =1 to ∞

K = 0 to n-1


n or k are not parts of each other.

Please explain in what context your are using n and k. Are they whole numbers, units of measure, or what?

(n AND k) is a complex that is based in building-block n and building-block k, such that n or k are not building-blocks of each other.

A doronComplex is something. I cannot comment on what it is until you explain what the building-blocks of n and k are.

You still closed under wiki and do not get the novel notion of Independent Membership, where atoms belongs to each other by their common property (which is the absence of building-blocks) but they are also independent of each other such that k belongs XOR does belong to n (it is local w.r.t n) and n belongs AND does not belong to k (it is non-local w.r.t k).

From what I remember (and from what wikipedia tells me) XOR is a either/or but not both type of comparison. You want us to see if n belongs to k. But if they are both atoms/ur-elements that you claim, then how can an ur-element be part of another ur-element?

The rest of your post is meaningless without you answering the questions.

How about you spend one post to answer all those questions.

 

[The Man]

The Man claims that y is true because it is an axiom of framework X.

Nope, but if "y" is true (or simply accepted as true) without the need (or possibility) of proof then it meets the definition of an axiom, such that it could be an axiom of “framework X” or some more developed “framework” X’. Try actually learning the concepts you want to base your arguments upon.

If it was the case, then y cannot be undecidable within axiomatic system X.

Well that was not the case. Are you now just going to conflate “undecidable” with un-provable or simply unproven?


Yep, sure enough, you are.

The only alternative is that y is a true theorem of X that is undecidable within axiomatic system X.

There is of course always that other alternative Doron, that you just conflate things so much that you end up just confusing yourself.

As a result we get an infinite extrapolation of X, such that y is undecidable by an infinite extrapolation of X.

Nope, your “y” was decidedly true (by you own assertions) in your “framework X”. Do you still want to conflate “undecidable” with un-provable or simply unproven?

Yep, sure enough, you do.

In other words, y belongs (it is a true theorem of X) AND does not belong to X (undecidable by an infinite extrapolation of X, or in other words, it is permanently beyond deductive systems of X extensions, and the non-locality of y theorem is clearly shown w.r.t deductive systems of X extensions).

Nope, still doesn’t help you obtain any consistency Doron. Since now you have just decided “y” “is a true theorem of X” (since it is unproven) yet claim it to be “undecidable”.

Strong deductive axiomatic systems (systems that are strong enough to deal with Arithmetic) must be consistent AND incomplete, according to Gödel’s incompleteness theorems, and the simplest solution for this result is the acceptance of Non-locality as a fundamental property of the mathematical science, in addition to its Local property.

This novel solution is seen in http://www.internationalskeptics.com/forums/showpost.php?p=5289082&postcount=6704.

No Doron, simply abandoning any semblance of consistency is certainly not a “novel solution” (at least on this forum). All you have done is to make your “novel solution” inconsistent and incomplete.

 

[The Man]

Can’t believe I almost missed this nonsense

No, Independent Membership is a novel notion that holds between atoms, where atoms are existing AND empty things.

Well since “Membership” depends on being, well, a member it is quite dependent. If you are simply referring to the fact that different members are independent in the sense that they are, well, different then that is simply trivial. Of course what makes them different is generally not what makes them members but what they share in common. However (as we went over on the other thread) even without anything else in common they would still share that lack of commonality. Membership is entirely dependent on how one defines what constitutes (and thus does not constitute) a member.

The result of the Independent Membership is a complex, where a complex is (Atom-A AND atom-B), such that the Atom-B property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-A, and Atom-A property of (Atom-A AND atom-B) prevents from (Atom-A AND atom-B) to be only Atom-B.

It is simply trivial Doron that A and B is not only A and/or not only B. Only you take this as some major revelation.

You will not find this novel notion in wikipedia, because wikipedia deals with already agreed things.

Probably because most people come to understand such trivially obvious notions quite early on, but we must remember your acquired your notions from kindergarten students.

Do not try to find the key in order to get OM under the already agreed street light.

Must be why you think you found your ‘OM key’ under the “street light” of disagreement, but still can’t see that your key disagreement is just with yourself.

In order to get OM you have to go beyond the already agreed, and this is the essence of a paradigm-shift, which in this case is inevitable.

The Man and jsfisher and The Man do not make the inevitable step to OM, and as a result they are not there and stay closed under the current paradigm, which is too weak in order to get OM’s reasoning.

I must be so nice; you just had to mention me twice.

Their failure to get OM is spread all along this thread.

That’s the failure of OM you see spread all over this thread, after being run over by the streetcar of consistency.

 

[doronshadmi]

Nope, but if "y" is true (or simply accepted as true) without the need (or possibility) of proof then it meets the definition of an axiom,

If yis an axiom of X, then Gödel’s incompleteness theorems have no case.

Gödel’s incompleteness theorems have a case exactly because y is a true theorem by the axioms of X that cannot be proved or disproved (it is undecidable by the axioms of X, and we permanently have to extend X in order to deal with y theorem.

As a result we get a consistent AND incomplete deductive framework, and this is exactly the result of Gödel’s incompleteness theorems, which you don’t grasp.

Again the rest of your replies are of the same “quality”.

Well since “Membership” depends on being, well, a member it is quite dependent.

It is true if Membership is between elements of a set.

It is not true if Membership is between atoms, and atoms are independent of each other, yet together they define a complex.

Again your weak reasoning can't get Independent Membership, and the rest of your post is based on this inability.

It is simply trivial Doron that A and B is not only A and/or not only B. Only you take this as some major revelation.

No The Man, it is simple and therefore profound.

Your use of “simply trivial” clearly demonstrates that you do not understand the fundamental difference between “Simple” and “Trivial”.

And because you do not get this difference then your ill reasoning actually enables (1-D AND 0-D) to be 0-D in
the case of 0.999...[base 10]=1.000...

Say no more.

 

[zooterkin]

The Man and jsfisher and The Man do not make the inevitable step to OM, and as a result they are not there and stay closed under the current paradigm, which is too weak in order to get OM’s reasoning.

So, Doron, what have you defined "inevitable" to mean, so that it makes sense in that sentence? Exactly how many have made this "inevitable" step?

 

[doronshadmi]

I thought that the Messiah Complex only applied to religion.

Why, are you the Messiah of non paradigm-shifts?

 

[doronshadmi]

So, Doron, what have you defined "inevitable" to mean, so that it makes sense in that sentence? Exactly how many have made this "inevitable" step?

Do you understand that (1-D AND 0-D), which is a complex, cannot be only 1-D (which is an atom or building-block), or only 0-D (which is an atom or building-block)?

If you logically understand it, then the understanding that no amount of (1-D AND 0-D) complexities is 1-D or 0-D, is logically inevitable.

In this case you do not need any external support that is based on “how many people get that?” in order to realize that it is logically inevitable.

Do you understand what I’v just said?

If you get that then you immediatly get that no amount of segments (1-D AND 0-D) is 1-D or 0-D, and one of the inevitable results
is that 0.999...[base 10] < 1.000... exactly by 0.000...1[base 10].

This is a paradigm-shift of both Standard and Non-standard Real Analysis (whether dafydd (http://www.internationalskeptics.com/forums/showpost.php?p=5296375&postcount=6731) likes it, or not).

There are scholars that are closly related to OM. One of them is Dr. Alan Rayner from the University of Bath (http://www.bath.ac.uk/mediaexpertise/alanrayner.html):

http://p2pfoundation.net/Inclusional_Research

http://people.bath.ac.uk/bssadmr/

http://www.inclusional-research.org/

Another scholar is Lere O. Shakunle the inventor of Transfigural Mathematics:

http://www.transfig-math.de/tmintro.htm

 

[doronshadmi]

then how can an ur-element be part of another ur-element?

By Independent Membership, no atom is a part of the other atom, and this is exactly the difference between Independent Membership and Dependent Membership, where element X is a sub-element of Y (which is not the case by Independent Membership where X is not a sub-element of Y and Y is not a sub-element of X, and together they define a complex).

For the third time, wiki will not help you in this case because wiki is not a source of novel ideas, and Independent Membership is a novel idea.