Deeper than primes

[dafydd]

I don't see the point either, maybe we should lerk from each other for a while.

Lerk?

 

[epix]

Conclusion:

Our initial assertion that there is a complete infinite set, is false.

You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize. That's why Homo habilis never made it to China, except for two: male and female.

 

[punshhh]

Lerk?

This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.

 

[epix]

This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.

Have you ever visited a crop circle?

 

[punshhh]

Have you ever visited a crop circle?

Yes, although at the time I didn't know what a crop circle was. It was before they were publicised.
I remember being puzzled, but didn't think much about it and carried on my walk.

 

[epix]

Yes, although at the time I didn't know what a crop circle was. It was before they were publicised.
I remember being puzzled, but didn't think much about it and carried on my walk.

What made you to enter the field? The curious indent or something else?

 

[punshhh]

What made you to enter the field? The curious indent or something else?

I was walking through a field of wheat off the path, not something folk do these days, but at the time I would walk anywhere.
I didn't see it until I walked into a straight part of the design about 2 feet wide.

Now I think about it I can't place the time or place, which is odd as I can see clearly in my memory the wheat lying flat on the ground.

 

[epix]

I was walking through a field of wheat off the path, not something folk do these days, but at the time I would walk anywhere.
I didn't see it until I walked into a straight part of the design about 2 feet wide.

Now I think about it I can't place the time or place, which is odd as I can see clearly in my memory the wheat lying flat on the ground.

So you didn't walk along the tramline. But what made you to enter the field in the first place?

 

[punshhh]

So you didn't walk along the tramline. But what made you to enter the field in the first place?

I did walk the tramline 10 or 20metres, I don't know if there were any other parts to it.

I really can't remember the occassion, it might have been walking Offa's Dyke path in the summer of 1981, on the Welsh borders.

 

[doronshadmi]

You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize.

This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".

My answer is:

"Even if all natural numbers are the members of the set of all natural numbers, this set exists exactly because there is an unclosed interval among the natural numbers, which guarantees the distinct existence of all natural numbers.

This unclosed interval demonstrates the incompleteness of any collection of distinct members, which enables the existence of distinct members, in the first place.

This fact is true for the set of all natural numbers, exactly as it is true for any possible collection with distinct objects, where one of these possible collections is the set of all real numbers.

Also this set has distinct members exactly because of the unclosed interval among the real numbers, which guarantees the distinct existence of all real numbers."

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

In other words, actual completeness is exactly the unclosed interval, and no collection of distinct objects can close it simply because actual infinity is beyond the magnitude of any given collection of distinct members.

Cantor missed The Actual infinity exactly because he wrongly defined it in terms another number system, called Transfinite numbers, which are still closed under the notion of collection of distinct objects.

But also among the Transfinite numbers there is an unclosed interval, which guarantees the distinct existence of all of them.

 

[dafydd]

This must be the result of me trying to debate something with you, rather like banging my head against a brick wall.

I suggest we stop banging our heads against this brick wall and take a more light hearted approach.

I was interested to hear how many instruments you play, do you play a folk repertoire?
My brother plays fiddle and guitar in a folk band doing gigs around the midlands.

Good on him.

 

[The Man]

Sounds like your riding on the back of a turtle.

Anyone else going to join you?

I have asserted no turtles, so whatever “Sounds” you are referring to in that regard certainly weren’t coming from me.

Anyone else going to join you?

Join me in what? Something you simply want to ascribe to me? Looks like you have already joined Doron in that particular propensity.

The Man's awareness is floating upon the surface of thoughts (emotionally and intellectually).

He does not have the needed simplicity to transcendent beyond the thoughts' process in order to be aware of the simplest state of awareness, which is the un manifested unified source of both physical and spiritual manifestations as a one organic realm.

See what I mean. Simply trying to ascribe some particular aspect of his own nonsense to someone else is already Doron’s forte. So unless you just want to join him in that, punshhh, I would recommend that you take a different tact.

 

[The Man]

This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".

My answer is:

"Even if all natural numbers are the members of the set of all natural numbers, this set exists exactly because there is an unclosed interval among the natural numbers, which guarantees the distinct existence of all natural numbers.

This unclosed interval demonstrates the incompleteness of any collection of distinct members, which enables the existence of distinct members, in the first place.

This fact is true for the set of all natural numbers, exactly as it is true for any possible collection with distinct objects, where one of these possible collections is the set of all real numbers.

Also this set has distinct members exactly because of the unclosed interval among the real numbers, which guarantees the distinct existence of all real numbers."

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

In other words, actual completeness is exactly the unclosed interval, and no collection of distinct objects can close it simply because actual infinity is beyond the magnitude of any given collection of distinct members.

Cantor missed The Actual infinity exactly because he wrongly defined it in terms another number system, called Transfinite numbers, which are still closed under the notion of collection of distinct objects.

But also among the Transfinite numbers there is an unclosed interval, which guarantees the distinct existence of all of them.

“In other words” simply meaning Doron has now replaced his “uncovered” line or line segment with an “unclosed interval” while still deliberately misusing the word “incompleteness” in reference to “any collection of distinct members”. Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.


Doron later asserts his “actual completeness is exactly” his “unclosed interval” the very aspect that he claims “demonstrates the incompleteness of any collection of distinct members”. So once again Doron simply, and perhaps deliberately, contradicts himself by claming that having his “unclosed interval” meaning his “actual completeness” , which he also claims is “beyond the magnitude of any given collection of distinct members”, is what “demonstrates the incompleteness of any collection of distinct members”. On the one hand “there is an unclosed interval among the natural numbers” that “demonstrates the incompleteness of any collection of distinct members”. While on the other hand his “actual completeness is exactly” that “unclosed interval” that is “beyond the magnitude of any given collection of distinct members.” As usual Doron remains the staunchest of just his own notions.

 

[The Man]

Says a person that has no knowledge about the science of consciousness, which mostly was developed in the Eastern world, for the past 5000 years.

Says a person that evidently has no knowledge about meaning of the word 'science'.

 

[epix]

Originally Posted by epix
You mean YOUR INITIAL ASSERTION. The evolution of human species has been merciful enough to extinct the part of the brain where the notion of "complete infinite set" could later materialize.

This part exists, for example, in The Man's and jsfisher's brains.

Because of this part they will ask you: "Please show a natural number that is not a member of the set of all natural numbers".

Your problem is that you don't read about math stuff enough to know that "all" doesn't have the sole function of a limiting quantifier, as it is almost always the case with the word's common use.

Examples of ALL:

I've been waiting all week to see her.

He had to walk all the way home.

She works all year round.

He'll need all the help he can get.

Someone took all the candy.

In math, especially in the set theory, "all" is not used as an explicit quantifier -- it is replaced by the word "finite" -- but it is used as a qualifier. Once you define an object, such a natural number, "all", as an adjective, relates to a set of those objects that have the property described by their definition. So the term "the set of all prime numbers" doesn't mean that Euclid got his proof regarding the infinitude of primes wrong and that The Man and jsfisher can't navigate around, as you believe so.

 

[doronshadmi]

“In other words” simply meaning Doron has now replaced his “uncovered” line or line segment with an “unclosed interval” while still deliberately misusing the word “incompleteness” in reference to “any collection of distinct members”. Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.


Doron later asserts his “actual completeness is exactly” his “unclosed interval” the very aspect that he claims “demonstrates the incompleteness of any collection of distinct members”. So once again Doron simply, and perhaps deliberately, contradicts himself by claming that having his “unclosed interval” meaning his “actual completeness” , which he also claims is “beyond the magnitude of any given collection of distinct members”, is what “demonstrates the incompleteness of any collection of distinct members”. On the one hand “there is an unclosed interval among the natural numbers” that “demonstrates the incompleteness of any collection of distinct members”. While on the other hand his “actual completeness is exactly” that “unclosed interval” that is “beyond the magnitude of any given collection of distinct members.” As usual Doron remains the staunchest of just his own notions.

The Man, you simply can't comprehend that "1-dimensional element" , "line", "unclosed interval", etc... is the same magnitude that enable smaller magnitudes to be distinguished from each other.

You get only the level of the smaller magnitudes, without being aware of the magnitude that actually enables the distinction of their elements.

Once again you demonstrate your weak logic, which can't get the co-existence of the non-local and the local as fundamental agents of Unity, which enable the existence of finite or infinite complexity.

Please read also http://www.internationalskeptics.com/forums/showpost.php?p=7111214&postcount=15197 .

Says a person that evidently has no knowledge about meaning of the word 'science'.

Without this fundamental understanding your science is no more than the surface level of the ocean of knowledge.

For example, by your surface-only reasoning you can't comprehend the following:

The Ocean is still the Ocean even if it is both calm (at the bottom level) AND not calm (at the surface level).

 

[doronshadmi]

Your problem is that you don't read about math stuff enough to know that "all" doesn't have the sole function of a limiting quantifier, as it is almost always the case with the word's common use.


In math, especially in the set theory, "all" is not used as an explicit quantifier -- it is replaced by the word "finite" -- but it is used as a qualifier. Once you define an object, such a natural number, "all", as an adjective, relates to a set of those objects that have the property described by their definition. So the term "the set of all prime numbers" doesn't mean that Euclid got his proof regarding the infinitude of primes wrong and that The Man and jsfisher can't navigate around, as you believe so.

epix, please read about Universal quantification ( http://en.wikipedia.org/wiki/Universal_quantification ), before you air your view about this subject.

The Universal quantification "for all" gets only the property of the quantity of distinct objects of some collection, without the needed understanding of what enables them to be distinct from each other, in the first place.

For example: The set of all real numbers does not exist if there is no co-existence between the non-local property of being real number AND the local property of being a particular real number.

This non-local property of being real number, is equivalent to the unclosed interval among particular real numbers.

In other words, no amount of particular real numbers is the non-particular (or non-local) property of being real number.

The rule is stronger than any collection of some particular expressions of it, which is a notion that can't be comprehended by a reasoning that gets only the amount of the particular expressions (the co-existence of rule\rule's expression is not understood by the quantitative-only western logic, which according to it, the rule is the sum of its particular expressions).

 

[epix]

epix, please read about Universal quantification ( http://en.wikipedia.org/wiki/Universal_quantification ), before you air your view about this subject.

The Universal quantification "for all" gets only the property of the quantity of distinct objects of some collection, without the needed understanding of what enables them to be distinct from each other, in the first place.

For example: The set of all real numbers does not exist if there is no co-existence between the non-local property of being real number AND the local property of being a particular real number.

This is sheer nonsense. Saying that A(upsidedown) gets only the property of the quantity of distinct objects of some collection," is inparsable, unless you define the term, "property of quantity," coz no such term exists outside your scribble.

Your example involving the set real numbers depends on your invention and general incorporation of locality, which needs a narrow definition.

Suppose that I say that there IS a coexistence between the non-local property of being real number AND the local property of being a particular real number. How are you going to prove otherwise without reverting to the argument of "serial-only, weak resoning?" You just can't formulate your statment in such a way that it would lead to a comprehensive proof.

 

[doronshadmi]

Additionally once again, apparently deliberately, ignoring that the set of all natural numbers is closed under an integer operation of succession, which is why “all natural numbers are the members of the set of all natural numbers”.

Here is some concrete example of The Man's "reasoning":

"the set of all natural numbers is closed under an integer operation of succession"

The proposition is wrong simply because any collection is actually open if succession is its inherent property, and this openness it true whether the succession is immediate, in the case of integers, or not immediate, in the case of rational or irrational numbers.

So, next time if some professional mathematician asks you to show some object that is not a member of its set, please ask him\her to show you the complete infinite set of these members, without ignoring the following facts:

1) One example at a time of some object that belongs to some infinite set, does not prove the completeness of that set.

2) Any infinite set exists exactly because succession (immediate or not) is its inherent property.

3) Succession among objects is possible only if there is an unclosed interval among them, otherwise there is not room for Succession, in the first place.

4) Without the interval among objects, there are no distinct objects in the first place, and the only possible set is the empty set.

 

[doronshadmi]

This is sheer nonsense. Saying that A(upsidedown) gets only the property of the quantity of distinct objects of some collection," is inparsable, unless you define the term, "property of quantity," coz no such term exists outside your scribble.

Really?

Please define the set of real numbers by ignoring the unclosed interval among then, which enables their distinction from each other.

Your example involving the set real numbers depends on your invention and general incorporation of locality, which needs a narrow definition.

You are talking about the set of real numbers, without providing the must have terms, which enable their existence in the first place, exactly because you are unable to understand the co-existence of a rule (non-locality) and its particular expressions (localities).

Suppose that I say that there IS a coexistence between the non-local property of being real number AND the local property of being a particular real number. How are you going to prove otherwise without reverting to the argument of "serial-only, weak resoning?" You just can't formulate your statment in such a way that it would lead to a comprehensive proof.

The rule exists at-once, in parallel, as non-locality among particular expressions (localities) of it, where no particular expression (locality) or collection of particular expressions (localities) is the non-local rule.

EDIT:

Any reasoning that ignores this co-existence, has no, so called, comprehensive proof(s) of this fine subject.