Deeper than primes

[The Man]

The Man,

Axioms are independent of each other (they are not derived from each other), yet they share the same framework by (hopefully) without derived to contradictions.

An axiom is considered to be independent only if it can not be proven by the other axioms of the “framework”. The “framework” as a whole is considered independent (or more specifically independently axiomatizable) only if each of the axiom is not provable by the remaining axioms. Again learn the actual concepts you are trying to base your arguments upon.

So "share" = "mutually" and "not derived from each other" = "independent", and we get exactly a Mutually Independent system.

The “framework or “system” is always dependent on the axioms, the independence only refers to the ability to prove a given or each axiom from the remaining axioms. However, I would not expect you to know or understand that since it is already a well established concept.

Again none of this helps your so called “independent membership” which would infer that the memberships are independent (not shared). What you are claiming, that elements sharing the same membership can be independent of each other (other than sharing that membership) is simply what I expressly mentioned before.

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 Man]

Through the eyes of a local-only thinker, this is exactly what you get.

Through the eyes of a loco-only thinker, the inconsistency of your OM is exactly what you do not get.

 

[doronshadmi]

Concerning your post, you do not have a professional relationship with those "scholars closely related to OM". I wonder why... Have you contacted them? If yes, what did they say about your OM? If not, why on earth not?

Yes, I have very interesting connections with them, and they think that OM is a very interesting theory.

 

[doronshadmi]

No, mathematicians do not have the option to choose whether arithmetic (or similar other formal system) is consistent or not. Please stop repeating this stupid notion.

Please stop your ignorence on this subject.

 

[doronshadmi]

Then your atoms are not “building-blocks” since they lack “building-blocks”, even just one.

Again you demonstrate your inability to get the idea of atom as an existing thing that has no sub-structure.

the independence only refers to the ability to prove a given or each axiom from the remaining axioms.

In order to compare between different things in order to realize that they are not derived form each other, we need a common environment.

So our considered realm is Mutually (common) Independent (no thing is derived form the other thing).

So Axiomatic framework is at least is Mutually (common) Independent framework.

For better understanding, please see please see http://www.scribd.com/doc/21954904/UP

 

[Little 10 Toes]

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.

Wow. Your reading and comprehension skills are pure rubbish. Let me explain it to you in little words. Perhaps you will get it this time.

1) You define n and k as numbers. I ask you to explain what n and k are. You do not. (see your above reply)

n =1 to ∞
K = 0 to n-1

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

2) You mention that the object "(n AND k)" is a complex and it is based on building-block n and building-block k. I ask you to explain what the building-blocks are. You do not. (see your above reply)

(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.

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

3)I ask you to answer my quesitons in one post. You do not. (see your above reply)

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

Let's try again with some basic questions.

• Using wikipedia's math definition: Is an atom the same as an ur-element? Yes/No
• Using wikipedia's math definition: Is an element or member of a set one of the distinct objects that make up that set? An element or member can be a unique set. Yes/No
• Can a set be a member of itself? Yes/No
• Do you know that when you have something that relies on two or more other things, that original something is dependent? For example, a peanut butter and jelly sandwich, is dependent upon having bread, peanut butter, and jelly. Yes/No
• If you disagree to the definitions, please explain why and state your own definitions clearly.
• What are n and k? (See statement #1)
• What are the building-blocks of n and k? (See statement #2)
• Please answer all these questions in one post. (See statement #3)

 

[doronshadmi]

make up your mind Doron

You see The Man, this is exactly your problem, too much makeup on your mind, until you
have lost your ability to see things beyond your makeuped mind.

This kind of makeup on your mind is based on XOR where no opposites can simultaneously be found at the same framework (the local-only reasoning).

For example: you can't get http://www.internationalskeptics.com/forums/showpost.php?p=5307896&postcount=6785.

 

[doronshadmi]

Wow. Your reading and comprehension skills are pure rubbish. Let me explain it to you in little words. Perhaps you will get it this time.

1) You define n and k as numbers. I ask you to explain what n and k are. You do not. (see your above reply)




2) You mention that the object "(n AND k)" is a complex and it is based on building-block n and building-block k. I ask you to explain what the building-blocks are. You do not. (see your above reply)





3)I ask you to answer my quesitons in one post. You do not. (see your above reply)



Let's try again with some basic questions.

• Using wikipedia's math definition: Is an atom the same as an ur-element? Yes/No
• Using wikipedia's math definition: Is an element or member of a set one of the distinct objects that make up that set? An element or member can be a unique set. Yes/No
• Can a set be a member of itself? Yes/No
• Do you know that when you have something that relies on two or more other things, that original something is dependent? For example, a peanut butter and jelly sandwich, is dependent upon having bread, peanut butter, and jelly. Yes/No
• If you disagree to the definitions, please explain why and state your own definitions clearly.
• What are n and k? (See statement #1)
• What are the building-blocks of n and k? (See statement #2)
• Please answer all these questions in one post. (See statement #3)

You make a hard time to yourself.

Again:

An atom is an existing thing that has not sub-things.

By OM there are two types of atoms:

1) A non-local atom, which its minimal form is an endless (or edgeless) straight line.

2) A local atom, which its minimal form is a point.

n = 1 to ∞

k = 0 to n-1

n-dim is non-local with respect to k-dim.

k-dim is local with respect to n-dim.

n-dim or k-dim are atoms (are not derived from each other).

(n-dim AND k-dim) is a complex, such that the n-dim of (n-dim AND k-dim) prevent from (n-dim AND k-dim) to be k-dim, and k-dim of (n-dim AND k-dim) prevent from (n-dim AND k-dim) to be n-dim.

 

[The Man]

Again you demonstrate your inability to get the idea of atom.

Again you demonstrate your inability to understand the importance of consistency.

In order to compare between different things in order to realize that they are not derived form each other, we need a common environment.

No, as stated before we just need the remaining axioms, which of course would differ depending on what axiom is removed for examination. Thus making the “environment” unique for each axiom being examined and it is certainly not “common“ to that particular axiom as that axiom is specifically excluded. Again learn the actual concepts you are trying to base your arguments upon.

So our considered realm is Mutually (common) Independent (no thing is derived form the other thing).

See here you go again you are using the “Mutually (common)” to refer to the “framework” or your purported “common environment” and the “Independent” to refer to the axioms, entirely inconsistent.

‘Mutually’ is an adjective just as ‘independent’ is, meaning they modify or give more information about a noun. The noun in this case can either be “framework” or “axiom” as using both is simply meaningless and inconsistent.

So Axiomatic framework is at least is Mutually (common) Independent framework.

No, again an “Axiomatic framework” can not be independent of its axioms, it is specifically based on those axioms. Whatever your “Mutually (common) Independent framework” is independent of it can not be its axioms. Again your are simply stringing together words into nonsensical, inconsistent gibberish.

For better understanding, please see please see http://www.scribd.com/doc/21954904/UP

For better understanding please see.

http://dictionary.reference.com

 

[The Man]

You see The Man, this is exactly your problem, too much makeup on your mind, until you
have lost your ability to see things beyond your makeuped mind.

This kind of makeup on your mind is based on XOR where no opposites can simultaneously be found at the same framework (the local-only reasoning).

For example: you can't get http://www.internationalskeptics.com/forums/showpost.php?p=5307896&postcount=6785.

More nonsensical gibberish Doron from you just stringing together words without rhyme or reason.

However one assertion is apparent.

This kind of makeup on your mind is based on XOR where no opposites can simultaneously be found at the same framework (the local-only reasoning).

You asserting quite plainly and clearly that contradiction is entirely the basis of your notions.

You will run into the same problem as you did in the other thread Doron that in attempting to formalize a Dialethism the very structure that permits contradictions also allows one to contradict that structure and your local/non-local ascriptions still remain meaningless

 

[jsfisher]

Please stop your ignorence on this subject.

If you can cite any evidence to contradict my statements, please do so. Knock yourself out.

But you can't, can you? You just make crap up, and you can't even convince yourself that any of your crap is real. Proof is your inability to define anything.

So, instead, you blame everyone else because your notions are a failure.

 

[sympathic]

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

All you are is a leech. http://en.wikipedia.org/wiki/Leech

 

[doronshadmi]

“Axiomatic framework” can not be independent of its axioms,

Axiomatics framework is not less than mutual AND independent properties in a one framework, which is something beyond yor makeup-logic.

 

[The Man]

Axiomatics framework is not less than mutual AND independent properties in a one framework, which is something beyond yor makeup-logic.

Again simply nonsensical gibberish resulting from you just stringing words together that you think sound significant. If you are simply asserting that a "framework" is "not less than" the " properties in" that "framework" then that is again simply trivial.

 

[The Man]

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

Indeed, you must say that it works because you simply can’t show that it works. Your “ideas” certainly have not developed, since you keep just repeating the same old nonsensical gibberish.

 

[doronshadmi]

Again simply nonsensical gibberish resulting from you just stringing words together that you think sound significant. If you are simply asserting that a "framework" is "not less than" the " properties in" that "framework" then that is again simply trivial.

Yes. I know that all your makeup-logic gets is trivial.

Since you are unable to get the notion of an atom, you also unable to get the notion of a complex.

An axiomatic framework is a complex; exactly as a ray or a segment are complexities.

For example:

Non-connected points are totally independent (isolated) of each other.

If a point is equivalent to an axiom, than no axiomatic framework exists if each axiom is totally independent (isolated) of the other axioms.

Also a segment has a line in addition to the endpoints (the axioms), where the line is the connector of the points. This property is the mutual aspect to the segment which is not total connectivity as an endless (edgeless) straight line is.

So an axiomatic framework is not total isolation (only point-like) or total connectivity (only line-like), but it is a complex where this complex is not totally connected (because of the independency of the axioms of each other) and not totally isolated (because of the mutuality (line-like property) that enables the compassion of the axioms with each other.

In other words, any axiomatic framework is a complex, which is at least mutual AND independent.

This beauty is beyond your makeup-logic.

 

[doronshadmi]

Indeed, you must say that it works because you simply can’t show that it works. Your “ideas” certainly have not developed, since you keep just repeating the same old nonsensical gibberish.

No mekupist can conclude anything about OM development.

 

[doronshadmi]

All you are is a leech. http://en.wikipedia.org/wiki/Leech

At lease a leech is a living thing, and not a dead embalm object (which is all you are) http://en.wikipedia.org/wiki/Embalming.

 

[doronshadmi]

If you can cite any evidence to contradict my statements, please do so. Knock yourself out.

But you can't, can you? You just make crap up, and you can't even convince yourself that any of your crap is real. Proof is your inability to define anything.

So, instead, you blame everyone else because your notions are a failure.

Very simple:

Since according to Gödel's incompleteness theorems (and because of the use of "for all" quantifier in strong systems that are able to deal with arithmetic) axiomatic system X cannot be Consistent AND Complete, then any mathematician that wishes to works with such strong system like X, has to choose between Consistency and Completeness. Most of (if not all) the mathematicians choose Consistency because strong AND complete axiomatic systems can prove A and not-A as true, and we get a non-interesting framework, which is naturally rejected by mathematicians.

 

[Little 10 Toes]

Let's try again with some basic questions.

• Using wikipedia's math definition: Is an atom the same as an ur-element? Yes/No
• Using wikipedia's math definition: Is an element or member of a set one of the distinct objects that make up that set? An element or member can be a unique set. Yes/No
• Can a set be a member of itself? Yes/No
• Do you know that when you have something that relies on two or more other things, that original something is dependent? For example, a peanut butter and jelly sandwich, is dependent upon having bread, peanut butter, and jelly. Yes/No
• If you disagree to the definitions, please explain why and state your own definitions clearly.
• What are n and k? (See statement #1)
• What are the building-blocks of n and k? (See statement #2)
• Please answer all these questions in one post. (See statement #3)

Evasion noted. Perhaps you cannot answer simple questions? So far, it appears you cannot.

You make a hard time to yourself.
Again:
An atom is an existing thing that has not sub-things.

By OM there are two types of atoms:
1) A non-local atom, which its minimal form is an endless (or edgeless) straight line.
2) A local atom, which its minimal form is a point.

n = 1 to ∞
k = 0 to n-1

n-dim is non-local with respect to k-dim.
k-dim is local with respect to n-dim.

n-dim or k-dim are atoms (are not derived from each other).

(n-dim AND k-dim) is a complex, such that the n-dim of (n-dim AND k-dim) prevent from (n-dim AND k-dim) to be k-dim, and k-dim of (n-dim AND k-dim) prevent from (n-dim AND k-dim) to be n-dim.

If I have two points, are they local or non-local to each other?