Deeper than primes - Continuation

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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.
Click to expand...

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.
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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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