Deeper than primes - Continuation

[doronshadmi]

The collection of natural numbers is clopen (where clopen, by a narrow view, means that the collection has minimal member but not maximal member).

First, let us use the narrow view of the clopen concept:

We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length, then we cut the circle at a point named 1, and transform the curved form into a clopen system of a straight line with a finite length (it is a clopen system because after the cut only one edge of the finite straight line is considered as the point that represent number 1).

Now the modular arithmetic form of all posible natural numbers along it, is rolled along the clopen finite straight line, where each tangent point is a 1-to-1 correspondence between the finite modular (circle) arithmetic form and the straight arithmetic form.

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Now, let us use the generalized view of the clopen concept:

Since both systems are clopen (by generalization no number is taken twice at each system), their accurate infinite cardinality is not satisfied.

Furthermore (now we are generalizing the notion of clopen by avoiding number's duplication along both circular and straight finite length forms), since a point along finite length (whether it has circular or straight form) represents one an only one number, then the clopen state holds for both circular and straight finite length forms, such that the accurate cardinality of Q or R is not satisfied.

Moreover, the order of the numbers, which are represented by points along both circular and straight finite length forms has no impact on the fact that both forms are clopen, and they are clopen because the cut is done at any given arbitrary point, which avoids number's duplication along both circular and straight finite length forms.

Since being clopen is a fact among any collection of distinct members, such collections (where their order is insignificant) do not have accurate infinite cardinality.

 

[realpaladin]

Wrong ( http://www.internationalskeptics.com/forums/showpost.php?p=8068121&postcount=524 )

That was before you started walking. From the moment you spouted gobbledigook again he clicked his ruby slippers and was gone.

 

[realpaladin]

The collection of natural numbers is clopen (has the minimal member but not the maximal member).

clopen...

Punshhh, sing me a song about that one...

 

[doronshadmi]

That was before you started walking. From the moment you spouted gobbledigook again he clicked his ruby slippers and was gone.

He does not use mathematical concepts as a part of his replies, so your argument is irrelevant.

 

[doronshadmi]

clopen...

Punshhh, sing me a song about that one...

You can't get that he avoids mathematical concepts in his replies.

Since you are not avoiding it, then please sing your song about http://www.internationalskeptics.com/forums/showpost.php?p=8074095&postcount=561 .

 

[jsfisher]

The collection of natural numbers is clopen

Except it isn't. Don't understand the term, clopen, either, do you?

We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length...

Oh, Doron, you skipped all the interesting details. Please show us exactly what you mean by "modular arithmetic form" since it is likely your usage is, well, non-standard. Use modulo 2. That would be the simplest for an example.

 

[punshhh]

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.

I have nothing to discuss with Doron for we are in agreement.

 

[realpaladin]

I have nothing to discuss with Doron for we are in agreement.

You have *NO* idea how loud that made me laugh!

 

[dafydd]

I have nothing to discuss with Doron for we are in agreement.

That made me laugh out loud too. In agreement about what? Explain Doron's theories to me and I don't mean his claim to be at one with unity. Explain his maths to me. Translate this gobbledygook for me please.

''We can take a modular arithmetic form where any possible natural number is represented by a given point along a finite length, then we cut the circle at a point named 1, and transform the curved form into a clopen system of a straight line with a finite length (it is a clopen system because after the cut only one edge of the finite straight line is considered as the point that represent number 1)''

 

[doronshadmi]

You have *NO* idea how loud that made me laugh!

The laugh of an ignorant mind, so?

 

[doronshadmi]

Some traditional mathematician skips all the interesting details, when he\she asks to represent infinitely many distinct members by finitely many distinct members (for example: modulo 2 is some case of a finite field), exactly because he\she does not understand that infinitely many distinct members along a finite length are clopen system, whether this finite length is a circle or a straight line.

 

[jsfisher]

Some traditional mathematician skips all the interesting details, when he\she asks to represent infinitely many distinct members by finitely many distinct members.

Ah! More evasion. We understand. You can't show your work because it doesn't work. Here, let me help you get started:

Arithmetic modulo 2 gives rise to two equivalence classes which we can represent using the conventional representative from each class, those being 0 and 1. We can map the natural number 0 to "modular arithmetic form" 0, and we can map the natural number 1 to "modular arithmetic form" 1.

There! I've got you started. Now, you try. What will be the mapping for natural number 2 in this bijection you claim exists?


You aren't ever going to get back to the original issue, either, are you? You know, where you asked that perfectly meaningless question, meaningless on two counts. You continue to distance yourself from that bit of stupidity on your part.

 

[doronshadmi]

As can be seen, traditional mathematics' modular arithmetic is restricted to finite amount of distinct members (some case of a finite field) along a circle.

As a result it can't deal with clopen systems as observed in http://www.internationalskeptics.com/forums/showpost.php?p=8074095&postcount=561 and can't get the answer given in http://www.internationalskeptics.com/forums/showpost.php?p=8071728&postcount=552.

B.T.W a ray is equivalent to clopen finite length.

 

[jsfisher]

As can be seen, traditional mathematics' modular arithmetic is restricted to finite amount of distinct members (some case of a finite field) along a circle.

As a result it can't deal with clopen systems as observed in http://www.internationalskeptics.com/forums/showpost.php?p=8074095&postcount=561 .

More evasion, but at least you continue to make it abundantly clear that you have virtually no understanding of Mathematics. A vocabulary of misused and invented terms is no substitute for knowledge.

Nonetheless, carry on. You've wasted all these many years of your life on your fantasy; without anything rational to fill the void you may as well continue with it.

 

[doronshadmi]

An evasion is noted each time Traditional Mathematics has to deal with its own limitations.

The slogan "understanding of Mathematics" is actually being closed under the limitations of Traditional Mathematics.

A limited vocabulary and the inability to re-define notions is no substitute for knowledge.

 

[jsfisher]

A limited vocabulary and the inability to re-define notions is no substitute for knowledge.

How hypocritical of the master of no definitions to make such a statement.

 

[doronshadmi]

Traditional Mathematics is the mastery of verbal_only anti-evolutionist embalmed definitions.

 

[jsfisher]

Traditional Mathematics is the mastery of verbal_only anti-evolutionist embalmed definitions.

Doron, this really is silly. You are acting like a kindergarten pupil on the playground. "Am not!" "Are too!"

You are going out of your way to avoid communication. You know it. We know it. We know you know it. And you know we know you know it.

Stop pretending.

If you have something to say, say it. But leave out the gibberish and the Doron-special meaningless terminology. If your goal really is to expose and discuss whatever revelation you have, you stupid antics are completely out of phase with that goal.

 

[doronshadmi]

Please look at the following diagrams ( http://www.math.rutgers.edu/~erowland/polygons-project.html ):

The distinct points on the perimeter are defined as long as the cardinality of the connected lines at each point is smaller by 1 than the cardinality of the points.

By pushing this system into actual infinity, no distinct points are defined anymore exactly because at actual infinity there is the power of the continuum, observed as 1-dimesional curved line (known as circle, in this case) which is not a collection of lower spaces (points) or sub-spaces (segments of curves).

 

[doronshadmi]

Traditional Mathematics can't rid of its traditional dogma in order to develop actual communication, because its dogma is context-dependent-only framework (no cross-contexts form is found).