Deeper than primes - Continuation

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"A line is a collection of points that extend forever." is a phrase given by verbal_symbolic-only reasoning.

The best minds in Cantor's time were verbal_symbolic-only skillers.

The flatterers of Traditional Mathematics are also verbal_symbolic-only skillers that simply can't grasp verbal_symbolic AND visual_spatial reasoning.

For example, such flatterer can't grasp an indivisible 1-dimensional space as a coordinator among coordinated 0-dimansional spaces, which are named by "0" and "1".
 
doronshadmi said:
"A line is a collection of points that extend forever." is a phrase given by verbal_symbolic-only reasoning.

The best minds in Cantor's time were verbal_symbolic-only skillers.

The flatterers of Traditional Mathematics are also verbal_symbolic-only skillers that simply can't grasp verbal_symbolic AND visual_spatial reasoning.

For example, such flatterer can't grasp an indivisible 1-dimensional space as a coordinator among coordinated 0-dimansional spaces, which are named by "0" and "1".
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It's amazing to see that you can't detect the super-sized contradiction in your statements.

Each n-dim space requires its own coordinate system for point definition. According to you, the x-line in the 1-dim Euclidian space
____________________________

is indivisible, because it creates the space. But if its length cannot be entirely covered by points, as you maintain elsewhere, then such an absence divide the line into line segments, so the line is therefore divisible by the absence of certain points on it
______ _______ __ _______ _____

which is the contradictory conclusion. There is other, purely mathematical consideration, which proves your statement about the incidence of gaps/absence of points in the real line false beyond any conceivable doubt. It has already been discussed, but due to your poor knowledge of basic arithmetic caused by your tremendous ignorance, it turned out ineffective, like anything else that walks into your House of Turbulent Reorganization of Multidimensional Reasoning.

Can you jump start your spatial_visual brain skills and draw the "1-dimensional space as a coordinator among coordinated 0-dimansional spaces" creature that lives in the attic of that house? I'd like to compare it with the results of Ezekiel's spatial_visual brain skills.
 
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Let's take for example some observation of some verbal_symbolic-only skiller.

It goes like that:

"There is other, purely mathematical consideration, which proves your statemenEach n-dim space requires its own coordinate system for point definition. According to you, the x-line in the 1-dim Euclidian space
____________________________

is indivisible, because it creates the space. But if its length cannot be entirely covered by points, as you maintain elsewhere, then such an absence divide the line into line segments, so the line is therefore divisible by the absence of certain points on it
______ _______ __ _______ _____

which is the contradictory conclusion."

This is an argument of a mind that can't comprehend the different levels of 1-dimensional space as an indivisible whole that is used as a coordinator among 0-dimensional spaces, where each 0-dimensional space is too weak in order to be a coordinator among more than a single 0-dimensional space (which is actually exactly only itself).

A segment is a composed result of whole\parts relations (or coordinator\coordinated relations) of two different levels of spaces, where each level is a non-composed (abstract or physical) realm, but verbal_symbolic-only skillers can't comprehend that, simply because in order to really comprehend that one has to use at least his\her verbal_symbolic AND visual_spatial brain skills.

By using verbal_symbolic AND visual_spatial brain skills one easily understands that 1-dimesnolal space is the indivisible coordinator among any amount of collection of composed objects like segments.

Again, the fundamental notion (that can't be comprehended by verbal_symbolic skillers) is that the whole is not a collections of any kind (whether it is a collection of non-composed elements like points or a collection of composed objects like line segments).

Here is another argument of this verbal_symbolic-only skiller:

"There is other, purely mathematical consideration, which proves your statement about the incidence of gaps/absence of points in the real line false beyond any conceivable doubt. It has already been discussed, but due to your poor knowledge of basic arithmetic caused by your tremendous ignorance, it turned out ineffective,..."

In this case this verbal_symbolic-only skiller demonstrates his\her inability to comprehend the notion of non-local numbers.

The failure of this verbal_symbolic only skiller is already discussed in http://www.internationalskeptics.com/forums/showpost.php?p=8646020&postcount=1997.

Traditional mathematicians and their groupies are still afraid to reason beyond their verbal_symbolic-only box

[qimg]http://thebsreport.files.wordpress.com/2009/10/cat-in-a-box.jpg?w=500&h=375[/qimg]
( http://thebsreport.files.wordpress.com/2009/10/cat-in-a-box.jpg?w=500&h=375 )

exactly because they refuse to be responsible for the possible results of their work (briefly discussed in http://www.internationalskeptics.com/forums/showpost.php?p=8498946&postcount=1811) .

As a result a post like http://www.internationalskeptics.com/forums/showpost.php?p=8646020&postcount=1997 goes beyond their mind.
 
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Little 10 Toes said:
Didn't miss ...
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You have missed the fact that results like 1+1=0 or 1+1=2 depend on your ability to determine a given framework, or in other words, the ability to determine a given framework means that you are a factor of the results, and being a factor of a given result is involved with responsibility.
 
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We have not missed the fact that you got nothing. Nada. Zilch. Rien. Nichts. कुछ नहीं.
 
doronshadmi said:
This is an argument of a mind that can't comprehend the different levels of 1-dimensional space as an indivisible whole that is used as a coordinator among 0-dimensional spaces, where each 0-dimensional space is too weak in order to be a coordinator among more than a single 0-dimensional space (which is actually exactly only itself).
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That's why I asked you to render your idea in a visually friendly way.

epix said:
Can you jump start your spatial_visual brain skills and draw the "1-dimensional space as a coordinator among coordinated 0-dimansional spaces" creature that lives in the attic of that house?
Click to expand...

But your compliance referred to a 3-D environment instead:
[qimg]http://thebsreport.files.wordpress.com/2009/10/cat-in-a-box.jpg?w=500&h=375[/qimg]
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So this is how I understand it. There is a 3-D space with coordinates b, o, and x, and inside the space is a 3-D object with coordinates c, a, and t. The polychotomic union of all coordinates seemingly creates a 6-D environment, but only seemingly, because when Novak-Splitzky cross product is considered, another 3-D object with coordinates CAT BOX is the result. In other words, you got http://fc06.deviantart.net/fs71/i/2011/021/6/c/cat_box_cake_by_ladyorange-d37qyq8.jpg, which is something that is often used to substitute number zero with by the visual_spatial-only skillers.
 
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doronshadmi said:
There is no chance that verbal_symbolic-only skillers can comprehend a given space > 0 not in terms of collection of objects.
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The diversity of the environment that you have mistakenly wandered into must be surely bewildering to you. Take for example Euclid's postulate regarding parallel lines.

350px-Parallel_Postulate.svg.png


But sometimes an unassailable notion can become questionable when it decides to leave it's natural habitat. On the road again...

road-perspective.jpg


Now it's your time to doom the misguided pagan Euclid using your elevated visual_spatial brain skills. Parallel lines do meet. Where? At the point of infinity, where else? Just grab the real line at -∞ and ∞ and turn the straight line into a circle. By doing so, you get RP1, or the real projective line.

220px-Real_projective_line.svg.png


That must have been a very inspiring development, because you used it to fix mathematics.

doronshadmi said:
6840987626_c9c426828a_z.jpg
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Not being able to grasp the concept, which allows division by zero only when the point of infinity is located at 12 o'clock, you placed the point at 3 o'clock; or you just primed the real projective line for your aggravated assault on reason. Then you garnished the drawing with your own definitions to the effect that reminds putting flowers on a grave.

But you did something very interesting: you added a semicircle whose origin can't be easily traced. The best assumption based on circumstances leads to the three semicircles below.

stock-illustration-759979-jewish-menorah-vector-card-1.jpg


If you claim having those brain skills wonderfully fused in such a way that it allows you the deepest insight into the world of abstract relationships where traditional math folks would perish, then you should be able to chose the semicircle that became the best suitable for your willful molestation of other people's ideas.
 
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The notion of point in infinity is exactly the inability of a verbal_symbolic-only skillers to understand that is below and above Membership, where Membership is closed under the concept of Collection.

The details are provided in part 3 (pages 8-9) of http://www.scribd.com/doc/98276640/Umes.

Please be aware of the novel notion of Riemann sphere there, which is beyond the verbal_symbolic-only abilities of the Traditional Mathematics' groupie.

Once again it is shown that verbal_symbolic-only skillers can't comprehend http://www.scribd.com/doc/98276640/Umes.
 
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doronshadmi said:
The notion of point in infinity is exactly the inability of a verbal_symbolic-only skillers to understand that is below and above Membership, where Membership is closed under the concept of Collection.
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Once again you proved beyond any doubt that your philosophy of pan-reductionism dwarfs Christianity. Point at infinity is an adjustment that makes such a point a real number and that's why in real projective geometry, the symbol for infinity is included in arithmetic operations, which you didn't bother to include in your twist'n'shout version.

There are different math concepts and none of them is superior to one another, as you think it is the case. The real line doesn't end under one concept of infinity and that's why you can't make a circle out of it, unless you badly need it. Since Homo sapiens is well-known for throwing away any concept no matter how holy it is when it doesn't fit his ever-increasing desires, like the real projective geometry, he turns the infinite into the finite-like and proceeds. But unlike in your case, he proceeds with consistency. Ponder the consequence regarding your type of species for yourself.
 
I reject the trivial notion of the biblical God that has to be worshiped by men.

In my opinion complex creatures like us have to develop their minds into Unity awareness, which enables them to be harmonious and creative in terms of entropic-free realm, where redundancy and uncertainty are challenges that shape their responsibility as factors of such realm.

As I get it, the bible was written by many persons with different levels of awareness to the silent source of thoughts, and so is the case about any minds' results (whether they are abstract or not) in any possible area, including Mathematics.

I think that the notion of a point at infinity ("... he turns the infinite into the finite-like ...") actually blocks the notion of entropic-free realm, which according to it a given space > 0 is not a collection of lower spaces.
 
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doronshadmi said:
I reject the trivial notion of the biblical God that has to be worshiped by men.

In my opinion complex creatures like us have to develop their minds into Unity awareness, which enables them to be harmonious and creative in terms of entropic-free realm, where redundancy and uncertainty are challenges that shape their responsibility as factors of such realm.

As I get it, the bible was written by many persons with different levels of awareness to the silent source of thoughts, and so is the case about any minds' results (whether they are abstract or not) in any possible area, including Mathematics.

I think that the notion of a point at infinity ("... he turns the infinite into the finite-like ...") actually blocks the notion of entropic-free realm, which according to it a given space > 0 is not a collection of lower spaces.
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Proof by Disbelief? That is usually not accepted as a rigorous proof method. It would help, too, if you relied less on gibberish and more on well-defined and well-understood terms.
 
Axiomatic notions do not need any proof, otherwise they can't be considered as axioms.

The axiomatic notion of point at infinity simply blocks the axiomatic notion of entropic-free (abstract or physical) realm, which according to it a given space > 0 is not a collection of lower spaces.

We have here an evolutionist competition between two axiomatic notions, where the traditional one stands at the basis of entropic (abstract or physical) realm (a given space > 0 is a collection of lower spaces), and the non-traditional one stands at the basis of entropic-free (abstract or physical) realm (a given space > 0 is not a collection of lower spaces).
 
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doronshadmi said:
Axiomatic notions do not need any proof, otherwise they can't be considered as axioms.
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That's great, except you haven't yet been able to articulate your axiom set for Doronetics. Nor does having your own private axiom set invalidate the rest of Mathematics.

The axiomatic notion of point at infinity simply blocks the axiomatic notion of entropic-free (abstract or physical) realm, which according to it a given space > 0 is not a collection of lower spaces.
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Gibberish, though it looks like you are trying to say that things which contradict your un-articulated axiom contradict your un-articulated axiom. That is strikingly not profound.

We have here an evolutionist competition between two axiomatic notions, where the traditional one stands at the basis of entropic (abstract or physical) realm (a given space > 0 is a collection of lower spaces), and the non-traditional one stands at the basis of entropic-free (abstract or physical) realm (a given space > 0 is not a collection of lower spaces).
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There is no competition. You haven't presented anything capable of competition. (And, again, even if you had, one new branch in Mathematics doesn't invalidate another.) All you have presented so far are various versions of word salad and out-right contradiction. Neither are foundation material for Doronetics.

As for the inevitable "you don't get it" you will soon post, you continue to confuse disagreement with misunderstanding. I, we, understand just fine that you present rubbish. At whatever point you prove capable of escaping gibberish, muddled thoughts, and blatant contradiction, then maybe you'll have something that isn't rubbish.

Until then, please remember my stuff works; yours, not so much.
 
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Once again, the axiomatic notion of point in infinity is exactly the inability of verbal_symbolic-only skillers to understand that is below and above Membership, where Membership is closed under the concept of Collection.

The details are provided in part 3 (pages 8-9) of http://www.scribd.com/doc/98276640/Umes.

Please be aware of the novel notion of Riemann sphere there, which is beyond the verbal_symbolic-only abilities of the traditional mathematicians in this thread.

Generally, it is shown that verbal_symbolic-only skillers can't comprehend http://www.scribd.com/doc/98276640/Umes.
 
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doronshadmi said:
Once again, the axiomatic notion of point in infinity is exactly the inability of verbal_symbolic-only skillers to understand that is below and above Membership, where Membership is closed under the concept of Collection.
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Give it up, Doron. Nobody is buying your vacuous dodge of blaming everyone else. You've got nothing to show for, what is it now, 30 years of self-delusion.

The details are provided in part 3 (pages 8-9) of http://www.scribd.com/doc/98276640/Umes.
Click to expand...

No details there. Just gibberish, confusion, and more self-delusion.

Please be aware of the novel notion of Riemann sphere there, which is beyond the verbal_symbolic-only abilities of the traditional mathematicians in this thread.
Click to expand...

Invariably, your "novel notions" of some established mathematical construct is nothing more than confusion and misunderstanding. This is no exception.

Generally, it is shown that verbal_symbolic-only skillers can't comprehend http://www.scribd.com/doc/98276640/Umes.
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You continually and willfully confuse disagreement for misunderstanding. We all understand just fine, Doron. It is you that is cognitively adrift. Your ideas are rubbish. Your ability to express your rubbish ideas is dreadful. Your comprehension of anything mathematical is abysmal.
 
Given any dimensional space, it is not composed by other spaces, but any association between dimensional spaces provides a composed realm.

For example, 0 dimensional space and 1-dimesional space are non-composed, but the result of the association between them provides composed objects like line segments.

The same principle holds between any possible association between non-composed dimensional spaces, which provide composed objects as the results of these associations.

By understanding the difference between the non-composed dimensional spaces and the associative composed results between them, one actually understands that no collection of lower spaces or collection of composed objects that are the results of the associations between dimensional space, has the power of the continuum of any non-composed dimensional space that is above these collections.

This understanding provides the accesses to entropic-free realm, that can't be known by the traditional notion of dimensional spaces, which is closed under the concept of Collection.

The result of this closeness is the inability to understand the inaccessibility of collections to the power of the continuum of the non-composed dimensional spaces > 0, which actually provides the fundamental terms in order to deal with entropic-free realm.

It has to be stressed that entropic-free realm is essential for further development of complex creatures like us.

Furthermore, since the associations between the non-composed dimensional spaces is derived from the Unity among them, and since Unity is the natural source of any non-composed or composed (abstract or physical) expression, complex creatures like us are able to interact among them in terms of harmonious and original creativity, which actually provides the natural consistency for any possible expression that is done by creatures with Unity awareness.

The creativity of creatures with Unity awareness is naturally challenged and being developed in terms of uncertainty and redundancy conditions, which are transformed from the current "problems and fears" state of mind into "challenge and joyfulness" sate of mind at the presence of vague conditions, which are the natural character of entropic-free (abstract or physical) realm.
 
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jsfisher said:
That's great, except you haven't yet been able to articulate your axiom set for Doronetics. Nor does having your own private axiom set invalidate the rest of Mathematics.
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The rules of blackjack can hardly invalidate the rules of poker, but it's not easy to navigate through Doron's gibberish to see his intention at this level. Doron would never reach the point where wrong premises can be fun to trace, like it is in the case of "vortex mathematics,"
http://vortexmath.webs.com/
not to speak about "solving" the Goldbach conjecture. Doron and his Ezekiel-like narration puts his effort most of the time well outside anything that even remotely resembles a common logical construct.
 
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The rules of survival of complex creatures like us in the long run, this is currently the main goal of modern science, where the mathematical science is not excluded.

This goal can't be achieved by any method that excludes us as factors of the possible results, and Traditional Mathematics definitely excludes the mathematicians as factors of the possible results.

Organic Mathematics is a preliminary example of a framework that does not exclude us as factors of the possible results under entropic-free realm.

Once again, we have here an evolutionist competition between two axiomatic notions, where the traditional one stands at the basis of entropic (abstract or physical) realm (a given space > 0 is a collection of lower spaces), and the non-traditional one stands at the basis of entropic-free (abstract or physical) realm (a given space > 0 is not a collection of lower spaces).

More details are provided in:

http://www.internationalskeptics.com/forums/showpost.php?p=8676785&postcount=2020

http://www.scribd.com/doc/97823738/Unity-Awarness

http://www.scribd.com/doc/98276640/Umes
 
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doronshadmi said:
The rules of survival of complex creatures like us in the long run, this is currently the main goal of modern science, where the mathematical science is not excluded.
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Ok, so you clearly have no concept of what science is nor about current research.

This goal can't be achieved by any method that excludes us as factors of the possible results, and Traditional Mathematics definitely excludes the mathematicians as factors of the possible results.
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Excellent example of a straw man. Otherwise, the sentence is without substance.

Organic Mathematics is a preliminary example of a framework that does not exclude us as factors of the possible results under entropic-free realm.
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Yeah, right. Doronetics is a complete failure. It is just a long brownian sequence of idiotic claims, contradiction, and gibberish, none of which is the stuff of frameworks, not even preliminary examples of ones.

Once again, we have here an evolutionist competition between two axiomatic notions, where the traditional one stands at the basis of entropic (abstract or physical) realm (a given space > 0 is a collection of lower spaces), and the non-traditional one stands at the basis of entropic-free (abstract or physical) realm (a given space > 0 is not a collection of lower spaces).
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As already noted in a previous post, this is completely wrong. There is no competition. Doronetics has no substance, let alone axiomatic basis. It's just an hodge-podge of lunacy like "entropic-free realm".

By the way, Doron, what axiom of real mathematics "stands at the basis of entropic (abstract or physical) realm (a given space > 0 is a collection of lower spaces)"? I think you just made that up. Prove me wrong.

More details are provided in:...
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Doron, your dissertations are devoid of meaningful content. They ramble from confused thought to confused thought without transition or logical inference. They start no where and wander aimlessly.
 
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The dogs bark, but the caravan goes on in order to explore environments beyond the traditional entropic closed (by point at infinity) box.
 
doronshadmi said:
The dogs bark, but the caravan goes on in order to explore environments beyond the traditional entropic closed (by point at infinity) box.
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Got nothing but empty metaphor and gibberish, eh, Doron?

You can't even address the points raised, and you let your bare-faced lie stand. Not very convincing, Doron. You also add yet another lie and contradiction to the mix since you were the one who introduced your tortured analogy to Riemann's sphere, complete with a point at infinity, into your diatribe.

Then again, Mathematics continues to work; doronetics, not so much.
 
To the traditional mathematicians here, please use your reasoning in order to consistently determine that (abstract or physical) 1-dimensional space has exactly 0 length, or (abstract or physical) 0-dimensional space has a length > 0.

If you do that, Organic Mathematics gets off stage.
 
doronshadmi said:
To the traditional mathematicians here, please use your reasoning in order to consistently determine that (abstract or physical) 1-dimensional space has exactly 0 length, or (abstract or physical) 0-dimensional space has a length > 0.

If you do that, Organic Mathematics gets off stage.
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As evidenced many times, you don't understand what the "traditional mathematician" means, and so you make a commensurate number of peculiar requests. We live in a 3-D physical space, so why don't you give the traditional mathematician an example of a physical 1-D space to let him better focus on your question?

Even Ezekiel had a better insight into the matter of complex spaces, than you have.

img49.jpg


This was the appearance and structure of the wheels: They sparkled like topaz, and all four looked alike. Each appeared to be made like a wheel intersecting a wheel.
Ezekiel 1:16

It takes Christian faith & common sense to advance Biblical mathematics:

ejp426347f1_online.jpg
 
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doronshadmi said:
The fact that there is 3-dimesional space does not prevent one to determine length in terms of lower dimensional spaces.

For example:

guitar-length.jpg

http://www.mathsisfun.com/measure/images/guitar-length.jpg

So, http://www.internationalskeptics.com/forums/showpost.php?p=8685398&postcount=2028.

Also be aware that your determination has to use also visual_spatial brain skills in addition to verbal_symbolic expressions.
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LOL. Now you call upon one out of the three coordinates that define a 3-D space to help you out with your physical 1-D space nonsense. So when you reformulate your initial question accordingly, the question asks the traditional mathematician to prove that guitars actually don't exist, nor does anything at all, for that jolly matter.

Why did you choose a guitar to demonstrate your incompetence?

I tell you why. The guitar is one of the objects that logically relates to "1-D." That's because there is only one D string available on that instrument.

openstrings.gif


Of course, you are totally incapable of forming such an association to prompt your choice, but someone else who's been hacking your mind is. And who might that be?

Every Adult Dog Growls Barks Eats

A dog is hacking your head?

We must consult the manual to weigh a realistic option...

I am the Alpha and the Omega, the First and the Last, the Beginning and the End.
Revelation 22:13

It looks like a comparison based on opposites other than Alpha and Omega... would be very instrumental:

Atheism is to Dog as Theism is to God.

Well, Heavenly Father, that's very good. Are we having fun yet?

I wish you could demonstrate your "omniscience" in other places than this board, which is infested with close-minded atheists. But let's play it safe, huh?

(Doron, God says that in order to gain real insight into mathematics and be capable of advancing the subject, you must milk the three-headed goat that grazes on reason in the Land of Tramtaria, until there is enough milk to form a lake and then you must walk on that milk 3 furlongs forth and 3 furlongs back.)
 
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Ho my Dog barks but the caravan goes on.

Length, in terms of 1-dimensional space is determined no matter how many values (starting by at least one value) are related to each one of (at least) some two different coordinates.

So, http://www.internationalskeptics.com/forums/showpost.php?p=8685398&postcount=2028.

Please be aware that if, for example, variable L is defined as the length of 1-dimensional space and variable P is defined as the length of 0-dimensional space in some verbal_symbolic-only mathematical expression, and L=0 or P>0, all you have is an inconsistent determination that is derived from verbal_symbolic-only brain skills (traditional mathematicians are closed under the illusion that abstraction is achieved if only verbal_symbolic brain skills are used).

Until this very moment the traditional mathematicians here did not provide the requested consistent determination (which can't be provided by using verbal_symbolic-only brain skills, as demonstrated above).
 
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doronshadmi said:
Please be aware that if, for example, variable L is defined as the length of 1-dimensional space and variable P is defined as the length of 0-dimensional space in some verbal_symbolic-only mathematical expression, and L=0 or P>0, all you have is an inconsistent determination that is derived from verbal_symbolic-only brain skills (traditional mathematicians are closed under the illusion that abstraction is achieved if only verbal_symbolic brain skills are used).
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Please be aware that your progressive decomposition of reason allows you to misrepresent not only what the traditional mathematician say, but what most of the folks that make up the human population say.

I wonder in which box - traditional or not traditional - Bernhard Riemann lives, according to your laws of segregation. That's because the arithmetic operations performed on the extended complex plane allow division by zero, like z/0 = ∞. That's a big no-no elsewhere.

Mathematics can define point as a potato pancake or a carrot stick, as long as it the definition keeps consistent throughout and produces logical results. So what are you trying to do? Pure math doesn't have in most cases any correspondence with the real world, so it can't perish under the weight of evidence.
 
Pure math doesn't have in most cases any correspondence with consistent reasoning if only partial brain skills (for example, only verbal_symbolic skills or only visual_spatial brain skills) are used.


Here is an example of verbal_symbolic-only reasoning.

Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.

General Formula: X2 + Y2 = r2 where r is the radius.

According to this verbal_symbolic-only reasoning, we still have a circle even if r=0 or r=∞, which is simply nonsense.


By using also visual_spatial brain skills, one easily understands that 0 = X2 + Y2 is the indivisible local building-block (0-dimensional space, in this case) and ∞ = X2 + Y2 is the indivisible non-local building-block (1-dimensional space, in this case), that if associated they provide a given circle.


So once again, http://www.internationalskeptics.com/forums/showpost.php?p=8686803&postcount=2032.
 
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doronshadmi said:
Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.
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You are wrong, Doron. Learn something about Mathematics before you try to correct it.

General Formula: X2 + Y2 = r2 where r is the radius.
Click to expand...

You are wrong, Doron. Learn something about Mathematics before you try to correct it.

According to this verbal_symbolic-only reasoning, we still have a circle even if r=0
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You are wrong, Doron. Learn something about Mathematics before you try to correct it.

...or r=∞
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You are wrong, Doron. Learn something about Mathematics before you try to correct it.


...which is simply nonsense.
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Ok, you got that correct. What you said, Doron, is simply nonsense.
 
Some traditional mathematicians have problems to understand that if the considered point is defined by two coordinates, so is the case about the set of all points that are at the same distance, r, from that fixed point. or in other words, all the considered points are on the same plane.

Moreover, the fact that all the considered points are on the same plane, is not changed by the used geometry (it can be Euclidean geometry or non-Euclidean geometry, it does not matter).

Also the fact that all the considered points are on the same plane, is not changed by the used formula (it can be Cartesian, Polar or Complex ( please see http://en.wikipedia.org/wiki/Circle )).


So again, here is an example of verbal_symbolic-only reasoning.

Definition of Circle

Definition: A circle is the set of all points on a given plane that are at the same distance, r, from a fixed point.

General (Cartesian) Formula: X2 + Y2 = r2 where r is the radius.

According to this verbal_symbolic-only reasoning, we still have a circle even if r=0 or r=∞, which is simply nonsense.


By using also visual_spatial brain skills, one easily understands that 0 = X2 + Y2 is the indivisible local building-block (0-dimensional space, in this case) and ∞ = X2 + Y2 is the indivisible non-local building-block (1-dimensional space, in this case), that if associated they provide a given circle.


So once again, http://www.internationalskeptics.com/forums/showpost.php?p=8686803&postcount=2032.
 
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Let's compare:

doronshadmi said:
Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.
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and this:

doronshadmi said:
Definition of Circle

Definition: A circle is the set of all points on a given plane that are at the same distance, r, from a fixed point.
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Your first statement, the one I commented on, is wrong. That fact that you didn't even notice, won't even admit, there is a significant difference between your first claim and now this second one tells us quite a lot about you, Doron. It reminds us you have poor reading skills, poor skills of expression, poor skills of reasoning, and overall sloppy thought processes incompatible with any achievement in Mathematics.

Please stop lecturing us on your claimed superior mental abilities. Your posts prove otherwise.
 
doronshadmi said:
Definition of Circle

Definition: A circle is the set of all points on a given plane that are at the same distance, r, from a fixed point.
Click to expand...

Ok, you finally transcribed a more complete version. Congratulations. You can now take the Advanced cut and paste techniques class.

General (Cartesian) Formula: X2 + Y2 = r2 where r is the radius.
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Nope, still wrong. It was wrong the first time you posted it. Adding "(Cartesian)" doesn't help. That fact you don't understand what is wrong is telling.

According to this verbal_symbolic-only reasoning, we still have a circle even if r=0
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Still wrong, but you will have trouble figuring out why.

...or r=∞
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Still completely wrong.

...which is simply nonsense.
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Still completely correct, but not about what you intended.
 
Again, some traditional mathematicians have problems to understand that if the considered point is defined by two coordinates, so is the case about the set of all points that are at the same distance, r, from that fixed point, or in other words, all the considered points are on the same plane in any possible system, in order to be considered as a circle by Traditional Mathematics.


So again, here is an example of verbal_symbolic-only reasoning.

Definition of Circle

Definition: A circle is the set of all points on a given plane that are at the same distance, r, from a fixed point.

General (Cartesian) equation: X2 + Y2 = r2 where r is the radius (it is general in the sense that we care only about the fact that the set of the considered points are on the same plane, no matter what is the exact position of the circle on the considered plane including the center point (which by this equation is 0,0 but this fact is insignificant to the considered argument)).

Some traditional mathematicians here still try to avoid the considered argument by claiming that (X-a)2 + (Y-b)2 = r2 (where (a,b) is the position of the center point on the considered plane) is significant to the considered argument, but their twisted maneuvers have no influence on the validity of the considered argument.

So once again, according to this verbal_symbolic-only reasoning (with or without all these twisted maneuvers), we still have a circle even if r=0 or r=∞, which is simply nonsense.


By using also visual_spatial brain skills, one easily understands that 0 = X2 + Y2 is the indivisible local building-block (0-dimensional space, in this case) and ∞ = X2 + Y2 is the indivisible non-local building-block (1-dimensional space, in this case), that if associated they provide a given circle (where the position of that circle on a given plane has no influence on the validity of the considered argument).


So once again, http://www.internationalskeptics.com/forums/showpost.php?p=8686803&postcount=2032.
 
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doronshadmi said:
Again, some traditional mathematicians have problems to understand that if the considered point is defined by two coordinates, so is the case about the set of all points that are at the same distance, r, from that fixed point, or in other words, all the considered points are on the same plane in any possible system, in order to be considered as a circle by Traditional Mathematics.
Click to expand...

You are really clueless, here, aren't you? You are floundering trying to double-speak your way around your blunders, but you don't even know what the blunders are.

Do keep trying, though. Circles aren't all the complicated. Moreover, once defined, the meaning is fixed, and no matter how much you, Doron, dislike the consequences of the definition, the definition doesn't yield to your incredulity.

Sucks to be you, trying once again to disprove a definition, and failing miserably, despite your amble deployment of straw men.
 
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