Deeper than primes

[jsfisher]

Very easy:

{} or {{}} are examples of finite sets.

{a,b,c,..} or {{a,b,c,...}} are examples of infinite sets.

Ah! So the secret is in the Axiom of the Ellipses.

Seriously, though, how will you be able to identify an infinite set in this your private mathematics of yours? For that matter, how do you propose to build a set theory that even includes infinite sets?

In both cases Set (represented by the outer "{" "}" ) is not a member of itself (its existence is non-local w.r.t any collection (finite or not) of members.

This has no relevance to my question.

 

[Apathia]

I said

The truth is out there.

What do you mean?

That has multiple layers of fun.

1.) Spaced out guy says, "Awsome man, the truth, it's like way out there!"

2.) Fox Mulder of the TV series X-Files says, "The occult truth, it's out there, and we're going to uncover it!."

3.) Doron says, "The Truth is Non-Local!"

Again, we do not have to use maximum Complexity. We use it according to our needs, but now we are aware of our limitations and do not take them as general cases.

Actually Organic Numbers is an open Complexity and my current system is also a limit case of Complexity exactly because no structure of localities is Non-locality.

Thank Goodness again!

Another way to get to that humility is to regard no conception or state of consciousness as absolute.

 

[jsfisher]

Ah! So the secret is in the Axiom of the Ellipses.

The Axiom of the Ellipses aside, let's see how the commonly accepted axiom sets for set theory fair under Doron's quantifier restrictions. The news is not good:

• Axiom of extensionality -- Nope.
• Axiom of foundation -- Nope.
• Axiom schema of restricted comprehension -- Nope.
• Axiom of pairing -- Nope.
• Axiom of union -- Nope.
• Axiom schema of collection -- Nope.
• Axiom of infinity -- Definitely nope.
• Axiom of power set -- Nope.

Even the Axiom of the Empty Set, unnecessary for ZF, isn't admissible. You aren't left with much of a basis for your set theory, Doron.

 

[Skeptic]

Like most mathematical cranks, Doron is fascinated by mathematical notation, showing little if any grasp of the underlying mathematical facts.

For example, he thinks that 1.0000.... just has to be different, somehow, than 0.999999.... -- they're written differently, aren't they? Conversely, he does not think he needs to define (or show the existence) of a difference between a finite and an infinite set. It is enough, for him, that he writes "..." somewhere.

In both cases, thinking that notation equals essence leads to ridiculous mistakes. In the first case, to thinking two different representations of the same real number (1) denote two different numbers, and in the second case thinking that {a,b,c...} and {{a,b,c...}} are infinite sets because of the magic of the "..." notation.

{a,b,c...} seems to have only 26 members (what comes after 'z'?). And, in any case, even if it were infinite -- or one used N instead ({1,2,3,...}) -- {{a,b,c...}} would still be a finite set, of course: it has a cardinality of 1, since it has one member -- the set {a,b,c...} -- and the latter's cardinality has no effect on the former's.

All of Doron's "mathematics" (such as it is) is based on similar confusion of notation with essence.

 

[sympathic]

Like most mathematical cranks, Doron is fascinated by mathematical notation, showing little if any grasp of the underlying mathematical facts.

To add to that, Doron has an even more serious problem. He refuses to accept that things mean differently than he understands them. Even when faced with hard fact evidence, he continues to hold his views. Also, his obsession with taking up well defined concepts, disagree with the concept and use the same term for his invented concept (like Set) confuses other who are not fluent in Math, and they actually think he knows what he is talking about.

 

[doronshadmi]

3.) Doron says, "The Truth is Non-Local!"

Worng.

I say that reseachable things are the result of Non-locality\Locality Linkage.

Thank Goodness again!

Another way to get to that humility is to regard no conception or state of consciousness as absolute.

Worng.

The atom is absolute, its expressions are not.

 

[doronshadmi]

Like most mathematical cranks, Doron is fascinated by mathematical notation, showing little if any grasp of the underlying mathematical facts.

For example, he thinks that 1.0000.... just has to be different, somehow, than 0.999999.... -- they're written differently, aren't they? Conversely, he does not think he needs to define (or show the existence) of a difference between a finite and an infinite set. It is enough, for him, that he writes "..." somewhere.

In both cases, thinking that notation equals essence leads to ridiculous mistakes. In the first case, to thinking two different representations of the same real number (1) denote two different numbers, and in the second case thinking that {a,b,c...} and {{a,b,c...}} are infinite sets because of the magic of the "..." notation.

{a,b,c...} seems to have only 26 members (what comes after 'z'?). And, in any case, even if it were infinite -- or one used N instead ({1,2,3,...}) -- {{a,b,c...}} would still be a finite set, of course: it has a cardinality of 1, since it has one member -- the set {a,b,c...} -- and the latter's cardinality has no effect on the former's.

All of Doron's "mathematics" (such as it is) is based on similar confusion of notation with essence.

http://www.scribd.com/doc/17039028/OMDP

http://www.internationalskeptics.com/forums/showpost.php?p=4992070&postcount=5627

 

[doronshadmi]

To add to that, Doron has an even more serious problem. He refuses to accept that things mean differently than he understands them. Even when faced with hard fact evidence, he continues to hold his views. Also, his obsession with taking up well defined concepts, disagree with the concept and use the same term for his invented concept (like Set) confuses other who are not fluent in Math, and they actually think he knows what he is talking about.

At the moment that Non-Locality is linked with Locality in your mind by Direct Perception, then and only then you have valuable things to say about my system.

 

[doronshadmi]

The Axiom of the Ellipses aside, let's see how the commonly accepted axiom sets for set theory fair under Doron's quantifier restrictions. The news is not good:

• Axiom of extensionality -- Nope.
• Axiom of foundation -- Nope.
• Axiom schema of restricted comprehension -- Nope.
• Axiom of pairing -- Nope.
• Axiom of union -- Nope.
• Axiom schema of collection -- Nope.
• Axiom of infinity -- Definitely nope.
• Axiom of power set -- Nope.

Even the Axiom of the Empty Set, unnecessary for ZF, isn't admissible. You aren't left with much of a basis for your set theory, Doron.

Non-locality\Locality Linkage that is based on Dirtect Perceprion, is the basis of axioms, so?

how will you be able to identify an infinite set in this your private mathematics of yours?

In an infinite set no member can be considered as a final member exactly because the amount of the members is not fixed.

In a finite set each member (if exists) can be considered as a final member exactly because the amount of the members is fixed.

The empty set is a finite set since the amount of its members is fixed.

 

[jsfisher]

http://www.scribd.com/doc/17039028/OMDP

http://www.internationalskeptics.com/forums/showpost.php?p=4992070&postcount=5627

It is ironic that doron provides links which support Skeptic's allegation, not refute it. It is even more ironic that the very first point the OMDP document attempts to make (1) No collection of 0-dim elements can completely cover a 1-dim element.) makes use of a quantifier doron has outlawed.

He asserts and rejects his own assertion all in the space of one simple sentence.

 

[Apathia]

Worng.

I say that reseachable things are the result of Non-locality\Locality Linkage.

Indeed you do say that. You also say that no collection is ever complete.
In that sense the Truth is always still out there.

Worng.

The atom is absolute, its expressions are not.

Correct. It was not a statement of your philosophical position.

It's another way of thinking that doesn't let one's concepts become a convict's ball and chain.

Most likely I am wrong. Reality is much more complex than my thinking and rationalizations.

 

[ddt]

{a,b,c...} seems to have only 26 members (what comes after 'z'?).

Oh, that's easy: {. See the ASCII table.

And, in any case, even if it were infinite -- or one used N instead ({1,2,3,...}) -- {{a,b,c...}} would still be a finite set, of course: it has a cardinality of 1, since it has one member -- the set {a,b,c...} -- and the latter's cardinality has no effect on the former's.

I shudder to the thought that I'd take any suggestion of Doron's serious, but from my cursory glance of the latest pages of this thread, it seems as if he wants to redefine cardinality of a set as, informally said, the size of the flattened set: when a member of said set is a set itself, you take its members into consideration, and apply this recipe recursively. Of course, you could define this formally (you and I could, doron can't), but the result would be very trivial; there being no Urelements in ZF, the size of all sets would be 0.

All of Doron's "mathematics" (such as it is) is based on similar confusion of notation with essence.

I generally apply the maxim "don't attribute to malice what can be attributed to ignorance", but with each post of doron's and each refutation thereof, I get more hesitant to do so. Doron would score more brownie points by admitting that what he wants is not cardinality and thus also coin another name for it. Oh, and show some willingness to actually listen to what people are saying.

 

[jsfisher]

Non-locality\Locality Linkage that is based on Dirtect Perceprion, is the basis of axioms, so?

As is your tendency, you missed the point completely. The question was never where'd the axioms come from. It was what were they. Without the quantifiers of which you disapprove, you will not be able to express any interesting axioms.

In an infinite set no member can be considered as a final member.

In a finite set each member can be considered as a final member.

Ok, great. And just how can you tell something is or is not a "final member", whatever that means?

I asked a really simple question, doron, and you have now muffed two attempts to answer it. Let's try again: Presented with some set, let's call it S, how can you classify it as being a finite or an infinite set?

 

[doronshadmi]

It is ironic that doron provides links which support Skeptic's allegation, not refute it. It is even more ironic that the very first point the OMDP document attempts to make (1) No collection of 0-dim elements can completely cover a 1-dim element.) makes use of a quantifier doron has outlawed.

No, it means exactly what it means:

A complete collection of localities does not exist, so?

 

[doronshadmi]

As is your tendency, you missed the point completely. The question was never where'd the axioms come from. It was what were they. Without the quantifiers of which you disapprove, you will not be able to express any interesting axioms.

I use "for all" but not on infinite sets, and as a result expose you trivial and flat game with sets, so?

 

[doronshadmi]

Ok, great. And just how can you tell something is or is not a "final member", whatever that means?

In an infinite set no member can be considered as a final member exactly because the amount of the members is not fixed.

In a finite set each member (if exists) can be considered as a final member exactly because the amount of the members is fixed.

The empty set is a finite set since the amount of its members is fixed.

 

[jsfisher]

No, it means exactly what it means:

A complete collection of localities does not exist, so?

That simple English sentence has no meaning in formal Mathematics without quantification over an infinite universe of discourse. Since you have prohibited such quantification, that simple English sentence and its formal counterpart are inadmissible to your private mathematics.

 

[doronshadmi]

That simple English sentence has no meaning in formal Mathematics without quantification over an infinite universe of discourse. Since you have prohibited such quantification, that simple English sentence and its formal counterpart are inadmissible to your private mathematics.

It is not English or Hebrew or any bla bla bla ...

It is Dircert Preception that stands at the basis of any bla bla bla ...

____ is not covered by any amount of . on it, Direct as that.

More details are given in http://www.scribd.com/doc/17504323/WZATRP8 .

 

[jsfisher]

In an infinite set no member can be considered as a final member exactly because the amount of the members is not fixed.

In a finite set each member (if exists) can be considered as a final member exactly because the amount of the members is fixed.

You are now three for three at failing to answer the question.

The empty set is a finite set since the amount of its members is fixed.

Your non sequitur raises the same question, but at the other of the spectrum. How can you formally define the empty set in your private mathematics without using a prohibited quantification? (English phrases such as "no members" or the equivalent cannot be used since it would entail a prohibited quantification.)

 

[jsfisher]

A complete collection of localities does not exist, so?

It is not English or Hebrew or any bla bla bla ...

I knew it wasn't Hebrew, and I was reasonably sure it wasn't any bla bla bla, but I really would have sworn it was a statement in English.

Thanks for the correction: Posts by doron are not in English. Got it.