Deeper than primes - Continuation

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punshhh said:
Yes.

There are other approaches to unity.
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There can be infinitely many approaches, but all of them are expressed from AND calm down into Unity, which is beyond any Polychotomy.
 
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doronshadmi said:
Only personal view (which is only at the level of thoughts, where thoughts are only subjective) is not Unity awareness.

Unity awareness is actual only if the calm non-subjective source (which is not in itself a thought) is not lost during all possible expressions (whether they are abstract of physical).
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doronshadmi said:
There can be infinitely many approaches, but all of them are expressed from AND calm down into Unity, which is beyond any Polychotomy.
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Yes I agree.
 
punshhh said:
Ah, you are acquainted with unity then, greetings.

Oh and by the way I don't want to be a Hindu, remember what I said about belief.
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Doron got this whole 'unity of thinginess' from when I pointed out transcendental meditation and the whole 'universal science' of the Maharishi out to him.

I think all of that balmy unity stuff is a load of cobblers... if you were to really try and find some more 'tools for the mind' you would have read the first thread as well were I explained why this unity stuff is utter nonsense.

And Hinduism doesn't factor into this. It is just that this guy, the one the Beatles smoked their Ganja with, found that he could get away from all the poverty and trash that 'unity proponents' so often generate.
 
doronshadmi said:
Despite of what has been written by you above, your awareness is trapped at the level of thoughts (you defiantly have no direct awareness of Unity).
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Your opinion is worthless since you are not convinced of it yourself; you are on a forum where people communicate using thoughts and words.

Either you are severely damaged in the brain or you are a schoolbook example of the Donning-Kruger effect (needs umlauts, I don't want to figure out how to type them on my tablet).
 
EDIT: Let's take a given circles' circumference as a 1-dimesiaonal space where all natural numbers are found along it as a collection of points (0-dimensional spaces).

EDIT: By using equal lengths of 1-dimesiaonal space between the points (where each point represents only once some natural number) we know that in terms of finite cardinality these clearly distinct points have opposite points (which are located at the half length of the circles' circumference) if the finite cardinality is even, or don't have opposite points (which are located at the half length of the circles' circumference) if the finite cardinality is odd.

Here is some example of odd or even cardinality ( http://britton.disted.camosun.bc.ca/modarith/modular/clocklogo2.gif (Original Web Site by Susan Addington)):

clocklogo2.gif


Even cardinality is seen by the blue and purple cases.

Odd cardinality is seen by the red and green cases.


In case of infinite cardinality, we actually can't determine if there is or there is no opposite point (some distinct natural number) which is located at the half length of the circles' circumference.


Question: Why is that, and what conclusions can be derived from this fact, about the nature of infinite cardinality?
 
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doronshadmi said:
Let's take a given circles' circumference as a 1-dimesiaonal spaces where all natural numbers are found along it as a collection of points (0-dimensional spaces).

By using equal sizes of 1-dimesiaonal spaces between the points (where each point represents only once some natural number) we know that in terms of finite cardinality these clearly distinct points have opposite points (which are located at the half length of the circles' circumference) if the finite cardinality is even, or don't have opposite points (which are located at the half length of the circles' circumference) if the finite cardinality is odd.

Here is some example of odd or even cardinality ( http://britton.disted.camosun.bc.ca/modarith/modular/clocklogo2.gif (Original Web Site by Susan Addington)):

[qimg]http://britton.disted.camosun.bc.ca/modarith/modular/clocklogo2.gif[/qimg]

Even cardinality is seen by the blue and purple cases.

Odd cardinality is seen by the red and green cases.

In case of infinite cardinality, we actually can't determine if there is or there is no opposite point (some distinct natural number) which is located at the half length of the circles' circumference.

Question: Why is that?
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Answer that question punshhh. Us lesser mortals are stuck at the level of thought.
 
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The Catholic Church has some odd cardinals. Is that what Doron's farrago of nonsense above is all about?
 
realpaladin said:
I think all of that balmy unity stuff is a load of cobblers... if you were to really try and find some more 'tools for the mind' you would have read the first thread as well were I explained why this unity stuff is utter nonsense.
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Well, as an awareness that is trapped only at the level of thoughts, Unity awareness is indeed utter nonsense, so?
 
doronshadmi said:
Let's take a given circles' circumference as a 1-dimesiaonal spaces where all natural numbers are found along it as a collection of points (0-dimensional spaces).
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You don't know the difference between a circle and its circumference, do you? (The question is purely rhetorical.)

...<mostly gibberish>...
In case of infinite cardinality, we actually can't determine if there is or there is no opposite point (some distinct natural number) which is located at the half length of the circles' circumference.


Question: Why is that?
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Two reasons. (1) You have elected a construction method that isn't appropriate for placing the entire set of natural numbers along a circle, and therefore the question you ask is meaningless. (2) The concepts of odd and even is applicable only to the integers, which the cardinality of the set of natural numbers is not, and therefore the question you ask is meaningless.
 
Some traditional mathematician may claim that I "have elected a construction method that isn't appropriate for placing the entire set of natural numbers along a circle".

EDIT: This is wrong, since the form of modular arithmetic is an appropriate way for placing the entire set of natural numbers along it.
 
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Some traditional mathematician may say that "The concepts of odd and even is applicable only to the integers, which the cardinality of the set of natural numbers is not"

This is also wrong since:

1) By traditional Mathematics Natural numbers are particular case of integers.

2) Traditional Mathematics uses mapping like:

1 <==> 2
2 <==> 4
3 <==> 6
4 <==> 8
...

or

1 <==> 1
2 <==> 3
3 <==> 5
4 <==> 7
...

in order to conclude things about infinite cardinality.
 
doronshadmi said:
Some traditional mathematician may claim that I "have elected a construction method that isn't appropriate for placing the entire set of natural numbers along a circle".

EDIT: This is wrong, since the form of modular arithmetic is an appropriate way for placing the entire set of natural numbers along it.
Click to expand...

Is this the best you can do for a back peddle? The method you described in the original post is not appropriate, cannot be used for the full set of natural numbers. The question you ended with is therefore, like most of what you post, without meaning.

Switching as you suggest in your edit quoted above gives a useless many-to-one mapping unrelated to your original meaningless question.

Are you really so confused that you cannot follow your own conversation? Don't answer. It has already been well established that you are.

I now predict a deliberate shift away from the original meaningless question by way of a sequence of quibbles and gibberish. You may now begin.
 
doronshadmi said:
Some traditional mathematician may say that "The concepts of odd and even is applicable only to the integers, which the cardinality of the set of natural numbers is not"

This is also wrong since:

1) By traditional Mathematics Natural numbers are particular case of integers.
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Nobody claimed otherwise. (And, by the way, "subset" was the word you wanted.)

2) Traditional Mathematics uses mapping like:

1 <==> 2
2 <==> 4
3 <==> 6
4 <==> 8
...

or

1 <==> 1
2 <==> 3
3 <==> 5
4 <==> 7
...

in order to conclude things about infinite cardinality.
Click to expand...

And what does that have to do with the concepts even and odd with respect to the cardinality of the set of natural numbers?
 
doronshadmi said:
Furthermore modular arithmetic is used by Traditional Math in order to describe the entire real-line, where integers a definitely included along it as ca be seen by the following diagram ( http://en.wikipedia.org/wiki/Point_at_infinity ):

[qimg]http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Real_projective_line.svg/200px-Real_projective_line.svg.png[/qimg]
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Sure. It is very easy to project the entire set of real numbers onto the points of a circle.

This has nothing to do with your original even/odd question. You are simply trying to distance yourself from the nonsense of that post.
 
A claim like "Switching as you suggest in your edit quoted above gives a useless many-to-one mapping" is utter nonsense since the modular arithmetic form has no impact on the mapping among natural numbers.
 
Please look at this question : "And what does that have to do with the concepts even and odd with respect to the cardinality of the set of natural numbers?"

It is related to the case where I show how Traditional Mathematics uses odds and evens w.r.t cardinality of the set of natural numbers, in order to conclude things about such cardinality, so the question is meaningless.
 
Also look at this reply: "This has nothing to do with your original even/odd question."

It is wrong since I clearly show how modular arithmetic deals with natural number, whether my model or the entire real-line is used.

In both cases the natural numbers are included along the form of modular arithmetic, which means that by the form of modular arithmetic the length between the natural number is not fixed.
 
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doronshadmi said:
A claim like "Switching as you suggest in your edit quoted above gives a useless many-to-one mapping" is utter nonsense since the modular arithmetic form has no impact on the mapping among natural numbers.
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So, you don't understand what a many-to-one mapping is. No surprise, really.

doronshadmi said:
Please look at this question : "And what does that have to do with the concepts even and odd with respect to the cardinality of the set of natural numbers?"

It is related to the case where I show how Traditional Mathematics uses odds and evens w.r.t cardinality of the set of natural numbers, in order to conclude things about such cardinality, so the question is meaningless.
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Another example of you not comprehending your own examples, I see. At no point did you relate the cardinality of the natural numbers to the even/odd concept.

doronshadmi said:
Also look at this reply: "This has nothing to do with your original even/odd question."

It is wrong since I clearly show how modular arithmetic deals with natural number, whether my model or the entire real-line is used.

In both cases the natural numbers are included along the form of modular arithmetic, which means that by the form of modular arithmetic the length between the natural number is not fixed.
Click to expand...

Two quibbles then finally this gibberish. As predicted.
 
doronshadmi said:
Some traditional mathematician may say that "The concepts of odd and even is applicable only to the integers, which the cardinality of the set of natural numbers is not"

This is also wrong since:

1) By traditional Mathematics Natural numbers are particular case of integers.

2) Traditional Mathematics uses mapping like:

1 <==> 2
2 <==> 4
3 <==> 6
4 <==> 8
...

or

1 <==> 1
2 <==> 3
3 <==> 5
4 <==> 7
...

in order to conclude things about infinite cardinality.
Click to expand...

So what?
 
jsfisher said:
Two quibbles then finally this gibberish. As predicted.
Click to expand...

Perhaps it will become clear when we all become one with Unity. Punshhh will no doubt be able to explain it. After all, he claims to know what Doron is rabbiting about.
 
Traditional Mathematicians do not understand that the nature of mapping among natural numbers is not changed by the form of modular arithmetic.

It means that also according to modular arithmetic there is bijection among the members of the, so called, the set of all natural numbers and proper subset of them (where odd or even numbers are some proper subsets of the, so called, the set of all natural numbers).

Yet we see that from the point of view of all natural numbers, Transnational Mathematics can't determine the construction of the entire natural numbers by the form of modular arithmetic, even if it supposed to do so (according to the current notions of Transnational Mathematics).

By modular arithmetic infinitely many points (and in this case the, so called, the set of all natural numbers) are included along a finite length, where no one of the points represents the cardinality of |N|, because it is greater than any represented finite cardinality along the finite length of the modular form.

So |N| is beyond the odd and even properties of the natural numbers (where these properties have a typical structure no matter how infinitely many cases of finitely many odd or even structures are involved) and it is clearly shown by the inability to determine if there is or there is no opposite point to some represented natural number along the finite length of a given circle.

This indeterminism is actually the inability (as some traditional mathematician says: "At no point did you relate the cardinality of the natural numbers to the even/odd concept") to define the accurate cardinality of the natural numbers, so |N| does not hold, and the whole idea of accurate transfinite cardinality is wrong.
 
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Once again, it has to be stressed that natural numbers are representable as points along a circle (where a circle is a finite length) and because a circle has a finite length, the position of the points (which represent the natural numbers) is not fixed among the infinitely many cases of odd or even constructions along the finite length.

As a result we have infinitely many constructions of natural numbers that can't determine if there is or there is no some natural number at the half length of the circles' circumference.

No |N| natural numbers can determine it exactly because |N| does not have an accurate value, or in other words, the whole idea of accurate transfinite numbers is wrong.

Let us look again at the real-line, where integers are definitely included along it as can be seen by the following diagram ( http://en.wikipedia.org/wiki/Point_at_infinity ):

[qimg]http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Real_projective_line.svg/200px-Real_projective_line.svg.png[/qimg]

1) ∞ can't be positioned along the circle (as wrongly illustrated above) because |R| is greater than any amount of points, which represent the real numbers along the modular model.

2) In the case of the modular arithmetic of the natural numbers, we are simply using a single direction of points along it, where also in this case ∞ can't be positioned along the circle because |N| is greater than any amount of points, which represent the natural numbers along the modular model.

So, weather rational or irrational numbers are represented between the points that represent the natural numbers, or not, the position of the points that represent the numbers (no matter what kind of numbers) is not fixed along the finite length of the modular arithmetic form.
 
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Since the position of points is not fixed along the finite length of the modular arithmetic form (which has only one direction) and since |N| is not represented by one of the points along the modular arithmetic form (we have a clopen system), then the existence of an opposite point at the half length of the circles' circumference is not determined and as a result |N| accurate value is not determined.

If we insist to define |N| as an accurate value, then we must also determine AND not determine the position of the opposite point at the half length of the circles' circumference, which is a contradiction, so |N| can't be accurate.
 
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doronshadmi said:
Traditional Mathematicians do not understand that the nature of mapping among natural numbers is not changed by the form of modular arithmetic.

It means that also according to modular arithmetic there is bijection among the members of the, so called, the set of all natural numbers and proper subset of them (where odd or even numbers are some proper subsets of the, so called, the set of all natural numbers).
Click to expand...

Nobody is disputing there is a bijection between the odd natural numbers and the full set of natural numbers. Are you arguing with yourself?

Oh course, this tie to modular arithmetic is a bit of Doron nonsense, but since it is fully irrelevant to the original point, it is unimportant.

As predicted, you've tried to quibble and use gibberish to distance yourself from that previous nonsense, but let's return to the original point, shall we, Doron? You tried to extrapolate from a mapping of a finite set onto equi-spaced points along a circle to a mapping of a countably infinite set. You also posed a meaningless question about the even- or odd-ness of the cardinality of a countably infinite set.

Care to show us how you'd map an infinite set onto equi-spaced points along a circle? Care to show us whether the cardinality of an infinite set is even or odd?
 
Please look at these questions of some traditional mathematician: "Care to show us how you'd map an infinite set onto equi-spaced points along a circle? Care to show us whether the cardinality of an infinite set is even or odd?"

By using modular arithmetic in order to represent the set of all natural numbers (which are represented as non-fixed positions along the finite length of a given circle) we realize that if infinitely many finite odd/even constructions are placed on the circle, we can't determine if the construction is even or odd, which means that the cardinality of the collection of infinitely many finite odd/even constructions can't be determined as an accurate value.

If we force accurate cardinality on the collection of infinitely many finite odd/even constructions along the finite length of the modular arithmetic form, we actually determine AND not determine the position of the opposite point at the half length of the circles' circumference, which is a contradiction.

Conclusion: The accurate cardinality of infinitely many finite odd/even constructions along the finite length of the modular arithmetic form is not satisfied, and since there is 1-to-1 correspondence between the points along the finite modular arithmetic form and an infinitely long straight line, this non satisfaction state holds for any arithmetic.

In other words, the whole idea of accurate transfinite cardinality is wrong.
 
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doronshadmi said:
By using modular arithmetic in order to represent the set of all natural numbers...
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Go ahead. Do it. Show us how you can use modular arithmetic to represent the set of all natural numbers. Use modulo 2. That should provide a convincing demonstration of your mastery of the subject.
 
Perhaps Doron's fan punshhh can throw some light on Doron's theories.
 
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dafydd said:
Perhaps Doron's fan punshhh can throw some light on Doron's theories.
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I am refraining from answering as well, since we are now in Religion and Philosophy and I am eager to see Doron and his sidekick Punshhh discuss some unity stuff.

But I stand by my prediction that Punshhh will be going the way all of Doron's sidekicks go... they support him for a bit but then mosey off when he starts following the yellow brick road again.
 
jsfisher said:
Go ahead. Do it. Show us how you can use modular arithmetic to represent the set of all natural numbers. Use modulo 2. That should provide a convincing demonstration of your mastery of the subject.
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You are evil. And I mean that in a good way. :)
 
realpaladin said:
I am refraining from answering as well, since we are now in Religion and Philosophy and I am eager to see Doron and his sidekick Punshhh discuss some unity stuff.

But I stand by my prediction that Punshhh will be going the way all of Doron's sidekicks go... they support him for a bit but then mosey off when he starts following the yellow brick road again.
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It was Doron's awareness of Unity shtick that drew punsssh in. Woo stuff like that attracts him like catnip attracts a cat. He soon found out that he was way out of his depth on the math.
 
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