Deeper than primes

zooterkin · Sep 22, 2011

doronshadmi said:
Since it is infinite it is also incomplete, according to my axiom.

And the difference between infinite and (Doron) incomplete is what, exactly?

doronshadmi · Sep 22, 2011

zooterkin said:
And the difference between infinite and (Doron) incomplete is what, exactly?

There is actual infinity, which is non-local AND non-composed, and there is potential infinity as understood, for example, in terms of collection of distinct objects, which is incomplete with respect to actual infinity.

The notion of potential infinity and its incompleteness, is explained in http://www.internationalskeptics.com/forums/showpost.php?p=7601080&postcount=16418 and http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420.

Again, no amount (finite or infinite) of ....... etc. has the power of continuum of ______

jsfisher · Sep 22, 2011

doronshadmi said:
There is...

Merely claiming the existence of something does not define it. Please answer zooterkin's question in a meaningful way.

epix · Sep 22, 2011

doronshadmi said:
In other words, if order does not exist among collections of distinct objects, then their distinct objects are not available.

For example, the expression "647+23" does not exist, since the objects of the collection of natural numbers are not available.

Available for what?

If there is no corresponding set of counting numbers organized in the strict ascending order, which bijects the distinct members of the primary set, then there is no way to select the 647th and the 23th member of the primary set, if the property responsible for the distinction (color, shape, and so on) cannot be used and the order in the set is left as the only option.

Your example doesn't make sense, coz the definition of N guarantees the existence of 647 and 23 in the set.

doronshadmi · Sep 23, 2011

jsfisher said:
Merely claiming the existence of something does not define it. Please answer zooterkin's question in a meaningful way.

Again, "define it" for you is done by using only verbal_symbolic skills.

By this restriction you can't comprehend definitions that are based on verbal_symbolic skills AND visual_spatial skills, as explained in http://www.internationalskeptics.com/forums/showpost.php?p=7601080&postcount=16418 and http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420.

Also you ignore again http://www.internationalskeptics.com/forums/showpost.php?p=7587585&postcount=16372.

doronshadmi · Sep 23, 2011

epix said:
Your example doesn't make sense, coz the definition of N guarantees the existence of 647 and 23 in the set.

Order has no significance among sets, for example:

N = {1,2,3,4,5,...} = {5,1,3,2,4,...}, where the only restriction is the strict distinction of the members.

jsfisher stronger claim of "no order" is criticized by me in http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420 , so if you have something to say about order, the right address for criticism is jfisher's stronger claim of "no order", which indeed has no sense.

epix · Sep 23, 2011

Originally Posted by epix
Your example doesn't make sense, coz the definition of N guarantees the existence of 647 and 23 in the set.

doronshadmi said:
Order has no significance among sets, for example:

N = {1,2,3,4,5,...} = {5,1,3,2,4,...}, where the only restriction is the strict distinction of the members.

So why did you threaten with

In other words, if order does not exist among collections of distinct objects, then their distinct objects are not available.

For example, the expression "647+23" does not exist, since the objects of the collection of natural numbers are not available.

Btw, what are "the objects of the collection of natural numbers?" I can imagine a collection of natural numbers, like 13, 18, 666, but what are the objects?

You surely have visions that Ezekiel would envy you.

doronshadmi · Sep 23, 2011

epix said:
Originally Posted by epix
Your example doesn't make sense, coz the definition of N guarantees the existence of 647 and 23 in the set.

So why did you threaten with

epix my claim is that "no order" is not the same as "order has no significance", and my claim about this subject is explained in http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420, which you still do not comprehend (according to your last replies about this subject).

Btw, what are "the objects of the collection of natural numbers?" I can imagine a collection of natural numbers, like 13, 18, 666, but what are the objects?

Infinitely many distinct objects of the same type as 13, 18, 666.

According to http://www.internationalskeptics.com/forums/showpost.php?p=7601080&postcount=16418 such collection is incomplete (please look also at http://www.internationalskeptics.com/forums/showpost.php?p=7601675&postcount=16422).

jsfisher · Sep 23, 2011

doronshadmi said:
Again, "define it" for you is done by using only verbal_symbolic skills.

This is untrue, but since you are so wrapped up in your confusion, you cannot see that. The issue is entirely that you, doron, are proficient in both verbal and visual gibberish, and little else. Your total inability to express yourself in any form of communication is your limitation, not ours. Just scribbling dots, curves, and arrows does not a definition make.

doronshadmi · Sep 23, 2011

jsfisher said:
Just scribbling dots, curves, and arrows does not a definition make.

jsfisher said:
This is untrue,

It is true, and your "Just scribbling dots, curves, and arrows" reply clearly demonstrates my argument about your inability to use visual_spatial skills in addition to verbal_symbolic skills at the basis of the Mathematical science reasoning.

epix · Sep 24, 2011

doronshadmi said:
epix my claim is that "no order" is not the same as "order has no significance", and my claim about this subject is explained in http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420, which you still do not comprehend (according to your last replies about this subject).

Your link doesn't include the statement that you disagree with; that is, "no order" is the same as "order has no significance."

Infinitely many distinct objects of the same type as 13, 18, 666.

I wonder about how large is the obfuscation factor in the way you present your ideas . . .
So you've defined those "objects" as "infinitely many distinct objects of the same type as the natural numbers. That's one helluva way to call the naturals.

How do you define the word "incomplete" with respect to the topic discussed?

jsfisher · Sep 24, 2011

doronshadmi said:
It is not "Just scribbling dots, curves, and arrows".

You are right. You provided a lot of other gibberish, too.

How's that definition for "to pick" coming along? Or maybe the one for "incomplete"? Or maybe the one for "local"? So many, many terms you abuse so freely, but never define.

doronshadmi · Sep 24, 2011

epix said:
Your link doesn't include the statement that you disagree with; that is, "no order" is the same as "order has no significance."

You are wrong, here it is:

doronshadmi said:
As for no order, for example, (AB,AB) really has no order (which is not the same as "order has no significance") exactly because the considered framework is under superposition of identities of 2-Uncertainty x 2-Redundancy Distinction Tree.

epix said:
I wonder about how large is the obfuscation factor in the way you present your ideas . . .
So you've defined those "objects" as "infinitely many distinct objects of the same type as the natural numbers. That's one helluva way to call the naturals.

epix, look what you wrote:

epix said:
Btw, what are "the objects of the collection of natural numbers?" I can imagine a collection of natural numbers, like 13, 18, 666, but what are the objects?

and my answer to what you wrote is short and simple:

doronshadmi said:
Infinitely many distinct objects of the same type as 13, 18, 666.

epix said:
How do you define the word "incomplete" with respect to the topic discussed?

By the inability of collection distinct objects to have to power of the continuum of the "host" mathematical space (for example: there is no homeomorphism between 0 dimensional space and 1 dimensional space), which is naturally non-local w.r.t the "hosted" collection.

The term "host" or "hosted" is used in order to clarify that the "host" space
is not made of the "hosted" spaces (for example: ______ (a 1 dimensional space) is not made of "_ _ _" or "......" (which are sub-objects) on it.)

doronshadmi · Sep 24, 2011

jsfisher said:
You are right. You provided a lot of other gibberish, too.

As long as your visual_spatial skills are not used in addition to your verbal_symbolic skills, you indeed have no choice but to get my arguments as gibberish.

jsfisher said:
How's that definition for "to pick" coming along?

Again, jsfisher.

How exactly you are using a phrase like "You still haven't explained why 17 cannot be picked twice from the set of integers" without understanding what a "pick" is?

jsfisher said:
Or maybe the one for "incomplete"? Or maybe the one for "local"? So many, many terms you abuse so freely, but never define.

Again your problem to use verbal_symbolic AND visual_spatial skills airs its limited view.

----------

Once again you ignore http://www.internationalskeptics.com/forums/showpost.php?p=7587585&postcount=16372.

Why is that jsfisher?

----------

By following jsfisher's "no order" argument about sets, one can't use the diagonal argument:

n1 = (1, 0, 0, 1, 0, 0, 0, ...)
n2 = (1, 1, 1, 1, 1, 1, 1, ...)
n3 = (0, 1, 0, 1, 0, 1, 0, ...)
n4 = (1, 0, 1, 1, 1, 1, 1, ...)
n5 = (1, 1, 0, 1, 0, 1, 1, ...)
n6 = (0, 0, 1, 1, 0, 0, 1, ...)
n7 = (1, 0, 1, 1, 1, 0, 0, ...)
...

n0 = (0, 0, 1, 0, 1, 1, 1, ...)

------------

By the way

{
(1, 0, 0, 1, 0, 0, 0, ...),
(1, 1, 1, 1, 1, 1, 1, ...),
(0, 1, 0, 1, 0, 1, 0, ...),
(1, 0, 1, 1, 1, 1, 1, ...),
(1, 1, 0, 1, 0, 1, 1, ...),
(0, 0, 1, 1, 0, 0, 1, ...),
(1, 0, 1, 1, 1, 0, 0, ...),
...
}

clearly demonstrates how the completeness of collection of distinct objects can't be satisfied (there are always more distinct objects (no matter how many distinct objects are defined) and this "always more distinct objects" permanent state is an inherent property of any infinite collection of distinct objects (in this particular example (0, 0, 1, 0, 1, 1, 1, ...) has to be added to the set, etc. ... ad infinitum ...).

Another example:

The "+1" expression of the axiom "If n is in N, then n+1 is in N" actually determines the inherent incompleteness of N.

The Man · Sep 24, 2011

doronshadmi said:
More than once, yes.

It is a conclusion derived from the following axiom:

If (x in C is picked) AND (everything but x, in C is picked) AND (x can't be picked twice), then C is infinite AND incomplete.

No it’s not; it is simply a result of you explicitly restricting the option of ‘picking’ a previous ‘pick’ to finite sets.

Again please define what you mean by “incomplete” particularly considering your new additions of “x in C is picked” and “everything but x, in C is picked”. What is left to be ‘picked’ when “x in C is picked” and “everything but x, in C is picked”?

doronshadmi said:
Please look at the axiom above, and explicitly show how it is related only to lists.

I’ll let you do that.

Since you’re apparently asserting now that you intend no relation only to lists, then ones previous ‘picks’ could be a set, either a proper subset of the super set or the super set itself?

doronshadmi said:
This is circular reasoning, since you have used "not finite" under "if" , and "infinite" under "then".

Again it is circular simply because you apply your restriction of not ‘picking’ from pervious ‘picks’ only for sets that are not infinite (or empty) and then claim the result, that “x can't be picked twice”, is what you define as that set being infinite. If you don’t like it then I suggest you put more effort into making better assertions.

doronshadmi said:
It took you less than a minute to come up with this circular reasoning.

See, once your deliberately couched and contrived langue was removed even you notice that you are simply claiming a set that you must already define as not finite and not empty is infinite, and it didn’t even take you 20 some odd years.

The Man · Sep 24, 2011

doronshadmi said:
Another example:

The "+1" expression of the axiom "If n is in N, then n+1 is in N" actually determines the inherent incompleteness of N.

Another deliberate misrepresentation would be more to the point, since the assertion is “then n+1 is in N”. Even if the assertion were “then n+1 is not in N” it wouldn’t make any difference as sets are complete simply by their definition. Again you still seem to be deliberately confusing a set for a list as a list need not be complete while a set always is complete as defined.

epix · Sep 24, 2011

Originally Posted by epix
Your link doesn't include the statement that you disagree with; that is, "no order" is the same as "order has no significance."

doronshadmi said:
You are wrong, here it is:

Originally Posted by doronshadmi
As for no order, for example, (AB,AB) really has no order (which is not the same as "order has no significance") exactly because the considered framework is under superposition of identities of 2-Uncertainty x 2-Redundancy Distinction Tree.

If I was wrong, then you disagree with yourself (follow the yellow line), but your repeated statement doesn't negate your claim. It follows that I couldn't be wrong.

You are chasing your tail; you are trying to justify your statement that honey is sweet, for example, but you can't find and present the opposing view.

jsfisher · Sep 24, 2011

doronshadmi said:
As long as your visual_spatial skills are not used in addition to your verbal_symbolic skills, you indeed have no choice but to get my arguments as gibberish.

The only one lacking spatial, visual, symbolic, and language skills is you, doron. Please stop projecting your inabilities onto others.

How exactly you are using a phrase like "You still haven't explained why 17 cannot be picked twice from the set of integers" without understanding what a "pick" is?

The sentence you quoted doesn't require I understand what you mean by "to pick", and you still haven't explained why 17 cannot be picked twice from the set of integers.

That aside, are you still going to dodge the question, or will you finally explain what you mean by this whole picking process? I'm betting you won't just because it is so much easier to make wild, baseless claims if you use words that have special meanings known only to you.

epix · Sep 24, 2011

doronshadmi said:
The "+1" expression of the axiom "If n is in N, then n+1 is in N" actually determines the inherent incompleteness of N.

You're affected by the frequent use of infinity where things approach ∞; you see a sequence where more and more members are added as the membership grows unbound. That's why you regard n as the temporarily last member in the process. But if you read again related Peano axiom

Every natural number a has a natural number successor

you may realize that n doesn't have to be necessarily the last number in the sequence in a given moment and that weakens your notion of "inherent incompleteness."

In the set theory, nothing approaches anything. The space in { } is populated instantly by items that have something in common by definition. One of the questions is how many items are in there. In the case of

{2, 4, 6, 8}

where all members are divisible by 2, which is a part of the defining terms, there are 4 members and the collection is complete as indicated by the brace } in the end. When the collection looks like this

{1, 2, 3, 4, ...}

and after it is clear what the expression stands for and the definition of the collection/set is stated (it is N), the question is how many items are in there. Since the whole expression includes the closing brace }, it is complete as well. So if it is complete, how many naturals do the braces hold?

One word that desribes the quantity in question became the most popular: aleph-null

You can come up with a Doronetics-compatible word describing the quantity.

Of course, you can choose a bolder approach by setting up your own definitions, like

S = {1, 2, 3, 4, ...

and call S "infinite AND incomplete." Then you should calculate the degree of incompleteness, coz that's what I'm really curious about.

doronshadmi · Sep 25, 2011

The Man said:
Another deliberate misrepresentation would be more to the point, since the assertion is “then n+1 is in N”. Even if the assertion were “then n+1 is not in N” it wouldn’t make any difference as sets are complete simply by their definition.

Your reasoning is restricted only to verbal_symbolic skills.

As a result you can't get "+1" expression, or the following axiom:

If (x in C is picked) AND (everything but x, in C is picked) AND (x can't be picked twice), then C is infinite AND incomplete.

For example, you ask:

The Man said:
What is left to be ‘picked’ when “x in C is picked” and “everything but x, in C is picked”?

You do not understand that everything in terms of collection (for example, points) can't reach the power of the continuum of non-local object (for example, a line), and you do not understand it exactly because your visual_spatial skills are not used in addition to your verbal_symbolic skills.

Again, you do not comprehend the inability of collections of distinct objects to have to power of the continuum of the "host" mathematical space (for example: there is no homeomorphism between 0 dimensional space and 1 dimensional space), which is naturally non-local w.r.t the "hosted" collection.

The term "host" or "hosted" is used in order to clarify that the "host" space
is not made of the "hosted" spaces (for example: ______ (a 1 dimensional space) is not made of "_ _ _" or "......" (which are sub-objects) on it.)

In other words, you still do not get http://www.internationalskeptics.com/forums/showpost.php?p=7601080&postcount=16418 or http://www.internationalskeptics.com/forums/showpost.php?p=7601467&postcount=16420.

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