Deeper than primes - Continuation

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epix said:
So you are saying that

1 - 3/9 = 6/9 = 2/3 > 0.666...10 by 0.000...666...10.
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Please show that 0.69 = 0.666...10 by using verbal_symbolic AND visual_spatial reasoning.


epix said:
Is this your handwriting?

When you make up your mind, let me know.
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When you stop to use old mistakes of mine in the current discussion (this time please follow after my corrections in http://www.internationalskeptics.com/forums/showpost.php?p=9332615&postcount=2596 of this old mistake of mine) you will be able to correctly understand my replies.


epix said:
You either misunderstood my question or can't do better than that. You mentioned the term "composed form." I googled up the term to get some clue of what that might resemble, but the only answer that ties "form" with "composed" is once again of musical nature.

http://en.wikipedia.org/wiki/Through-composed#Form

I do believe that there is some comprehensive link between the music and your terminology, because the adjective in "Organic Mathematics" relates to the word organ, which in turn is strongly linked with music - the nice music in particular:


That particular organ playing is comprehensively linked with the concept of fractals, which play (no pun intended) a leading role in your composed or non-composed spaces, because the word "fractal" is etymologically married to "fracture" or to "break apart."

I think that Organic Mathematic terminology is too demanding as far as an association formation is concerned - it calls for too much visual_spacial work. Can you come up with something less complicated?
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You either misunderstood my answers or can't do better than that.

The right way to do better than that is to use verbal_symbolic AND visual_spatial reasoning in order the understand the axiomatic expression, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632.
 
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doronshadmi said:
In http://www.internationalskeptics.com/forums/showpost.php?p=9347627&postcount=2640 you wrote


so please show how 0.69 = 0.666...10 by using verbal_symbolic AND visual_spatial reasoning.

This is the reason(ing) behind my request. Can you use it?
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It's still a request without a reason for it given. But if it means something to you, then I have to disappoint you, because "verbal_symbolic AND visual_spatial reasoning" is a terminology which lacks necessary substance and this type of "reasoning" cannot be applied outside of Organic Mathematics. Standard math doesn't use any esoteric method to do a number base conversion. But we can compare notes: do the conversion above with the help of the verbal_symbolic AND visual_spatial reasoning, and then I show you the normal, quick method that does the same job.
 
epix said:
It's still a request without a reason for it given. But if it means something to you, then I have to disappoint you, because "verbal_symbolic AND visual_spatial reasoning" is a terminology which lacks necessary substance and this type of "reasoning" cannot be applied outside of Organic Mathematics. Standard math doesn't use any esoteric method to do a number base conversion. But we can compare notes: do the conversion above with the help of the verbal_symbolic AND visual_spatial reasoning, and then I show you the normal, quick method that does the same job.
Click to expand...

Epix, verbal_symbolic-only reasoning lacks necessary substance and this type of "reasoning" cannot be applied outside of Standard Mathematics (which excludes infinitesimals).

Standard math uses a degenerate axiomatic method (which excludes infinitesimals) to do a "number base conversion". By this degenerate axiomatic method the place-value method (that uses some base > 1) provides only numerals of a given number, and these numerals are no more than some representation method (out of infinitely many other representations methods) where no representation is the represented number in itself (according to the degenerate axiomatic method, as clearly expressed, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9328741&postcount=2562).

So there is no way to convert representations into a number system by Standard Mathematics (which excludes infinitesimals).

You simply continue to ignore, for example, http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632, and as result you actually have no case about the discussed subject.

Again, by Standard Mathematics (which excludes infinitesimals) 0.999...10 or 0.111...2 or 0.222...3 etc. ad infinitum, are no more than different numerals (representations) of the same number, which is 1, in this case, where the used expression (by Standard Mathematics (which excludes infinitesimals)) , in this case is:

0.999...10 = 0.111...2 = 0.222...3 = 1, where only 1 is the number in itself, and 0.999...10 or 0.111...2 or 0.222...3 are no more than some of its numerals.

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On the contrary, by using the non-degenerate axiomatic method (that uses verbal_symbolic AND visual_spatial reasoning), expressions like 0.999...10 or 0.111...2 or 0.222...3 etc. ad infinitum, are numbers, where according to this reasoning, the following expression is valid:

0.111...2 < 0.222...3 < 0.999...10 < 1
 
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doronshadmi said:
Epix, verbal_symbolic-only reasoning lacks necessary substance and this type of "reasoning" cannot be applied outside of Standard Mathematics (which excludes infinitesimals).

Standard math uses a degenerate axiomatic method (which excludes infinitesimals) to do a "number base conversion". By this degenerate axiomatic method the place-value method (that uses some base > 1) provides only numerals of a given number, and these numerals are no more than some representation method (out of infinitely many other representations methods) where no representation is the represented number in itself (according to the degenerate axiomatic method, as clearly expressed, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9328741&postcount=2562).

So there is no way to convert representations into a number system by Standard Mathematics (which excludes infinitesimals).
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Leibniz and Newton would turn in their graves if they read the result of your observation.
http://www.encyclopediaofmath.org/index.php/Infinitesimal_calculus

Note that math in the link doesn't involve numbers displayed in the radix format, the one that you limit your results to, because Organic Mathematics doesn't know how to convert those results into the closed, or exact form. You need to learn that to avoid cumbersome expressions unkind to algebra. You need to learn that so your arguments wouldn't be infested by bad math manners. 78 F - 27 C is a meaningless statement, unless the temperature scale conversion is done. When you write that a difference is equal to 0.69 - 0.666...10, leave it to the reader to do the conversion, and when he does it, you ask him to convert it again using some "spatial_visual reasoning," then it is clear that you are mathematically delinquent.

Why don't you show me how that "degenerate axiomatic method" works? I believe that you are substantially misguided.

You simply continue to ignore, for example, http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632, and as result you actually have no case about the discussed subject.

Again, by Standard Mathematics (which excludes infinitesimals) 0.999...10 or 0.111...2 or 0.222...3 etc. ad infinitum, are no more than different numerals (representations) of the same number, which is 1, in this case, where the used expression (by Standard Mathematics (which excludes infinitesimals)) , in this case is:

0.999...10 = 0.111...2 = 0.222...3 = 1, where only 1 is the number in itself, and 0.999...10 or 0.111...2 or 0.222...3 are no more than some of its numerals.

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

On the contrary, by using the non-degenerate axiomatic method (that uses verbal_symbolic AND visual_spatial reasoning), expressions like 0.999...10 or 0.111...2 or 0.222...3 etc. ad infinitum, are numbers, where according to this reasoning, the following expression is valid:

0.111...2 < 0.222...3 < 0.999...10 < 1
Click to expand...

Your inequalities and equalities got nothing to do with number base conversion itself; they relate to the interpretation of the results. Click once again on the link above and you'll see an expression n→∞ in there without the word limit. And so

For n→∞ (...): 0.111...2 < 0.222...3 < 0.999...10 < 1

whereas

For limit n→∞ (...): 0.111...2 = 0.222...3 = 0.999...10 = 1

See how deficient your radix system-only is in general? I can't use the condition n→∞, because your inequalities lack a particular variable and the progress toward infinity is indicated just by the ellipses (...), which is a symbolism that doesn't distinguish between n→∞ and limit n→∞. And there is a crucial difference.

Now do the number base conversion of 0.69 to a10, so we can compare the methods of conversion.

Listen, is this number 22990631(dec.) familiar to you?

No?

But it will be, because

DORON36 = 2299063110

is the number on the door of your room in the Spatially Visual Facility for Delinquent Mathematicians.
 
epix said:
Leibniz and Newton would turn in their graves if they read the result of your observation.
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You are invited to show infinitesimals in jsfisher's "Actual Mathematics".

epix said:
Note that math in the link doesn't involve numbers displayed in the radix format, the one that you limit your results to, because Organic Mathematics doesn't know how to convert those results into the closed, or exact form.
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Wrong. Organic Mathematics axiomatically provides (http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632) the difference between non-composed numbers (do not have ...) and infinitely composed numbers (do have ...), so nothing has to be converted EDIT: (as can be seen, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9328458&postcount=2559).

epix said:
You need to learn that to avoid cumbersome expressions unkind to algebra.
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You need to use also visual_spatial reasoning, which enrich Algebra.

epix said:
You need to learn that so your arguments wouldn't be infested by bad math manners. 78 F - 27 C is a meaningless statement, unless the temperature scale conversion is done. When you write that a difference is equal to 0.69 - 0.666...10, leave it to the reader to do the conversion, and when he does it, you ask him to convert it again using some "spatial_visual reasoning," then it is clear that you are mathematically delinquent.
Click to expand...
By not using also visual_spatial reasoning (Some example of its use: http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632) you simply understand mathematics only only in terms of verbal_symbolic reasoning.

epix said:
Why don't you show me how that "degenerate axiomatic method" works? I believe that you are substantially misguided.
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It excludes infinitesimals, and for more information please look at Standard (Real) Analysis.


epix said:
Your inequalities and equalities got nothing to do with number base conversion itself; they relate to the interpretation of the results. Click once again on the link above and you'll see an expression n→∞ in there without the word limit. And so

For n→∞ (...): 0.111...2 < 0.222...3 < 0.999...10 < 1

whereas

For limit n→∞ (...): 0.111...2 = 0.222...3 = 0.999...10 = 1

See how deficient your radix system-only is in general? I can't use the condition n→∞, because your inequalities lack a particular variable and the progress toward infinity is indicated just by the ellipses (...), which is a symbolism that doesn't distinguish between n→∞ and limit n→∞. And there is a crucial difference.
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You are still missing it, according to Organic Mathematics, a non-composed number like 1 is the limit of a composed number like 0.111...2

It means that:

1) 0.111...2 can't be > limit 1

2) Since limit 1 level is inaccessible to 0.111...2 level, then 0.111...2 can't be but < limit 1


epix said:
Now do the number base conversion of 0.69 to a10, so we can compare the methods of conversion.
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You are still using notions that are derived from verbal_symbolic-only reasoning.

So I'll ask you again, can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Please answer only by Yes or No to this question.
 
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doronshadmi said:
Wrong. Organic Mathematics axiomatically provides (http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632) the difference between non-composed numbers (do not have ...) and infinitely composed numbers (do have ...), so nothing has to be converted.
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So why don't you convert 0.6666371371371... into a closed/exact (p/q) form step by step as an example? Such a demonstration would be more than beneficial for a method comparison. Your link doesn't associate with the decimal-to-exact conversion in question at the slightest.

You need to use also visual_spatial reasoning, which enrich Algebra.
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Your links rarely display variables and closed forms which makes algebra what it is.

By not using also visual_spatial reasoning (Some example of its use: http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632) you simply understand mathematics only only in terms of verbal_symbolic reasoning.
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You don't need any "enhanced" methods to deal with stuff known in antiquity.

It excludes infinitesimals, and for more information please look at Standard (Real) Analysis.
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Real analysis also deals with derivatives and integrals,
http://www2.stetson.edu/~mhale/real/
and where are derivatives and integrals, there must be infinitesimals.
http://en.wikipedia.org/wiki/Differential_(infinitesimal)
You are clearly not in control of the works, are you?

It means that:

1) 0.111...2 can't be > limit 1

2) Since limit 1 level is inaccessible to 0.111...2 level, then 0.111...2 can't be but < limit 1
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If I were interested in an example of circular reasoning, I would have asked.

You are still using notions that are derived from verbal_symbolic-only reasoning.

So I'll ask you again, can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Please answer only by Yes or No to this question.
Click to expand...

The answer is No, Doron. I will not marry you, for my religious affiliation (Strictly Hard Uncompromising Literal Atheism) prevents me to do so.
 
doronshadmi said:
You are invited to show infinitesimals in jsfisher's "Actual Mathematics".
Click to expand...


The original foundation of The Calculus exploited infinitesimals. Do you not realize this?

On the other hand, the nonsense you have spewed of late doesn't involve infinitesimals.
 
jsfisher said:
The original foundation of The Calculus exploited infinitesimals. Do you not realize this?
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And your "Actual mathematics" "correct" this original foundation, by exclude infinitesimals, isn't it?

jsfisher said:
On the other hand, the nonsense you have spewed of late doesn't involve infinitesimals.
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Your "Actual mathematics" excludes infinitesimals because it is too weak in order to deal with them (as explained in http://www.internationalskeptics.com/forums/showpost.php?p=9350072&postcount=2645).
 
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doronshadmi said:
And your "Actual mathematics" "correct" this original foundation, by exclude infinitesimals, isn't it?
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No. And what does this have to do with the nonsense you have been spewing?

Your "Actual mathematics" excludes infinitesimals because it is too weak in order to deal with them (as explained in http://www.internationalskeptics.com/forums/showpost.php?p=9350072&postcount=2645).
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No. And what does this have to do with the nonsense you have been spewing?


What you are implying is that 1.000... - 0.999... = delta, where delta is an infinitesimal. Is that what you seriously mean?
 
jsfisher said:
No. And what does this have to do with the nonsense you have been spewing?



No. And what does this have to do with the nonsense you have been spewing?
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Yes, and it is related to your deceleration about infinitesimals in http://www.internationalskeptics.com/forums/showpost.php?p=9302818&postcount=2433.

jsfisher said:
What you are implying is that 1.000... - 0.999... = delta, where delta is an infinitesimal. Is that what you seriously mean?
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Please to not play the ignorant. You know exactly what I mean.

Edit:

Can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Please answer only by Yes or No to this question.
 
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doronshadmi said:
Yes, and it is related to your deceleration about infinitesimals in http://www.internationalskeptics.com/forums/showpost.php?p=9302818&postcount=2433.
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Naive set theory has its own dark corners of contradiction, too. So? It doesn't mean it is without utility, but it does mean its use must be mindful of its limitations.

But I ask yet again, what does this derail about infinitesimals have to do with Doronetics?

Please to not play the ignorant. You know exactly what I mean.
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I see. You don't know what you mean, either.
 
jsfisher said:
Naive set theory has its own dark corners of contradiction, too. So?
Strawman, jsfisher.

It doesn't mean it is without utility, but it does mean its use must be mindful of its limitations.
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Again your one level reasoning is used by ignoring http://www.internationalskeptics.com/forums/showpost.php?p=9302818&postcount=2433.

jsfisher said:
But I ask yet again, what does this derail about infinitesimals have to do with Doronetics?

I see. You don't know what you mean, either.
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Can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Please answer only by Yes or No to this question.
 
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doronshadmi said:
Can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?
Click to expand...

Your question doesn't parse. ETA: Your aren't being responsive to the question asked of you. Instead you point us at other nonsense while claiming it has some special properties it does not have.


Be that as it may, what does this derail about infinitesimals have to do with Doronetics? Are you claiming 1.000... - 0.999... = some infinitesimal?
 
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jsfisher said:
Your question doesn't parse.

Be that as it may, what does this derail about infinitesimals have to do with Doronetics? Are you claiming 1.000... - 0.999... = some infinitesimal?
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Yes, and the details (using base 2 without loss of generality) are given in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632.

So I'll ask you for the last time, and please answer only by Yes or No:

Can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Any answer which is different than Yes or No, will be considered as evasion.
 
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doronshadmi said:
Yes, and the details (using base 2 without loss of generality) are given in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632.
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Excellent! So you finally admit 1.000... and 0.999... are indistinguishable, or you don't understand infinitesimals at all. (Smart money is on the latter.)

So I'll ask you for the last time, and please answer only by Yes or No:

Can you add also visual_spatial reasoning to verbal_symbolic reasoning, as done, for example, in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 ?

Any answer which is different than Yes or No, will be considered as evasion.
Click to expand...

Conclude what you like. The question doesn't make much sense and it is an irrelevant derail.
 
jsfisher said:
Excellent! So you finally admit 1.000... and 0.999... are indistinguishable,
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In your degenerate axiomatic dreams, simply because any given infinitesimal > 0.

A number system is said to be Archimedean if it contains no infinite or infinitesimal members.
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(http://en.wikipedia.org/wiki/Infinitesimal)

In other words, your "Actual Mathematics" is simply a framework that is restricted by the Archimedean property.

Organic Mathematics is not restricted by the Archimedean property, exactly because given any collection that is a mixture of at least two different non-composed dimensional spaces, no amount of members of that collection is accessible to the non-composed property of these non-composed dimensional spaces.


jsfisher said:
The question doesn't make much sense and it is an irrelevant derail.
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In your degenerate axiomatic dreams.

An evasion has been noted.
 
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doronshadmi said:
Organic Mathematics is not restricted by the Archimedean property
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No, doronetics is not restricted by anything, including logic, reason, any kind of formal axiomatic system or even a single proof of anything.

Quite the achievement. Of course, monkeys typing on typewriters could do the same all day long. Hell, they might even get lucky and type something of value.
 
laca said:
No, doronetics is not restricted by anything, including logic, reason, any kind of formal axiomatic system or even a single proof of anything.

Quite the achievement. Of course, monkeys typing on typewriters could do the same all day long. Hell, they might even get lucky and type something of value.
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This is indeed the best conclusion of a person that can't distinguish between potential infinity at the level of composed mathematical spaces, and actual infinity at the higher level of a given non-composed mathematical space > 0.

More details (using base 2 without loss of generality) about this mathematical universe, which is not restricted by the Archimedean property, are given in http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632.
 
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epix said:
78 F - 27 C is a meaningless statement, unless the temperature scale conversion is done.
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epix, the difference between the two values on a given thermometer is not changed (by using also visual_spatial reasoning), whether you convert the measurement units into one system or the other, for example:

thermometer1.jpg

(http://ipcblog.org/wp-content/uploads/2010/08/thermometer1.jpg)
 
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Let's define Locality and Non-locality in the most general way.

A) The definition of Locality:

If X is entirely at Y, then X is local w.r.t Y.


B) The definition of Non-locality:

If X is not entirely at Y, then X is non-local w.r.t Y.


An example of (A): A given point X is entirely at line Y.

An example of (B): A given line X is not entirely at point Y.


(A point or a line are undefined, similarly to Hilbert's approach)
 
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Let's improve the previous post.


A) The definition of Locality:

If non-composed X is entirely at non-composed Y, then non-composed X is local w.r.t non-composed Y.


B) The definition of Non-locality:

If non-composed Y is not entirely at non-composed X, then non-composed Y is non-local w.r.t non-composed X.


An example of (A): A given point X is entirely at line Y.

An example of (B): A given line Y is not entirely at point X.


(A point or a line are undefined symbolically similarly to Hilbert's approach, but unlike Hilbert's approach they are understood spatially)

According to (A) and (B) no amount of localities entirely covers a given non-composed Y, since given a collection of all non-composed X's at non-composed Y, non-composed Y is not entirely at any given non-composed X.

In other words, any given collection is no more than a potential infinity w.r.t a given non-locality.
 
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doronshadmi said:
According to (A) and (B) no amount of localities entirely covers a given non-composed Y, since given a collection of all non-composed X's at non-composed Y, non-composed Y is not entirely at any given non-composed X.

In other words, any given collection is no more than a potential infinity w.r.t a given non-locality.
Click to expand...


Neither statement follows from your definitions (even ignoring their inadequacies).
 
doronshadmi said:
Let's improve the previous post.


A) The definition of Locality:

If non-composed X is entirely at non-composed Y, then non-composed X is local w.r.t non-composed Y.


B) The definition of Non-locality:

If non-composed Y is not entirely at non-composed X, then non-composed Y is non-local w.r.t non-composed X.


An example of (A): A given point X is entirely at line Y.

An example of (B): A given line Y is not entirely at point X.


(A point or a line are undefined symbolically similarly to Hilbert's approach, but unlike Hilbert's approach they are understood spatially)

According to (A) and (B) no amount of localities entirely covers a given non-composed Y, since given a collection of all non-composed X's at non-composed Y, non-composed Y is not entirely at any given non-composed X.

In other words, any given collection is no more than a potential infinity w.r.t a given non-locality.
Click to expand...

X at local non-locality Y is locally non-local and mappable on composed local localities.
 
jsfisher said:
Neither statement follows from your definitions (even ignoring their inadequacies).
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You can't grasp the notion that Y is non-composed even if there is another non-composed X entirely at its domain, isn't it jsfisher?

By simply spatially understand, for example, a point at the domain of a line, one easily understands that a line is not a composition of points.

Since your visual spatial abilities are not used when you are doing Math, what you wrote above, is the best you can do.
 
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dafydd said:
X at local non-locality Y is locally non-local and mappable on composed local localities.
Click to expand...

''A little learning is a dangerous thing''-Alexander Pope, and this is exactly what you are doing, in the considered case.
 
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doronshadmi said:
You can't grasp the notion that Y is non-composed even if there is another non-composed X entirely at its domain, isn't it jsfisher?
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No, not at all. The problem is with your leap from a simple, albeit clumsy definition to a grandiose conclusion. You provided no logical path of reason that gets you from "Local means" to "and therefore".

So, as I said, your conclusions do not follow from your definition.

But then again, theorems seldom follow from definitions. Usually axioms and other theorems provide the basis for a new theorem.

Still, you want to just make stuff up then imagine it to be true, knock yourself out. Spend another several years of your life getting absolutely nowhere with this pet gibberish of yours.


Tell me this, Doronshadmi: Would a 40 unit line segment qualify as a non-composed object, or are only points and full lines allowed into this exclusive club?
 
jsfisher said:
Tell me this, Doronshadmi: Would a 40 unit line segment qualify as a non-composed object, or are only points and full lines allowed into this exclusive club?
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Tell me this, jsfisher: why you are unable to understand that the 1 dimensional space of a given line segment is not entirely at the domain of a given 0 dimensional space on it, exactly because the 1 dimensional space of that segment is non-composed?

jsfisher said:
You provided no logical path...
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Wrong, your classical logic is local-only, for example, by this logic, to be AND not to be at a given location is considered as a contradiction.

By understanding, for example, a line w.r.t a given point on it, no contradiction is involved, exactly because this is the very nature of a non-local element (which can't be known from your local-only reasoning).

Spend your entire life getting absolutely nowhere with this local-only reasoning of yours (for example, http://www.internationalskeptics.com/forums/showpost.php?p=9342098&postcount=2632 is not at the scope of your local-only reasoning).
 
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jsfisher said:
If you can't answer my question, just say you don't know.
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Actually you don't understand your own question exactly because you get everything only in terms of collections.

By not being restricted to your degenerate classical reasoning, one easily understands that a given length of a non-composed line segment is not changed even if the endpoints on it or even the collection of all points along that given non-composed line segment, are omitted.

It is a straightforward notion (that can't be deduced by the collection-only reasoning) that no real number (which is equivalent to a non-composed 0-dimesional space) contributes anything to a given length > 0.

Moreover, from the non-composed view of, for example, 1-dimesional space, the exact length of 0.999...10 is not satisfied, because the exact location of the non-local number 0.999...10 (which is a composition of 0 AND 1 dimensional spaces) along a given 1-dimesional space, is not satisfied.

Again, a collection of 0-dimensioal spaces (known also as real numbers along a given line segment) do not contribute anything to the length of that given line segment exactly because it is a non-composed 1-dimesional space, that is at AND not at the location of any given 0-dimesional space (or a composition of 0 AND 1 dimensional spaces like, for example, the non-local number 0.999...10) along it.

The term clopen line segment is enriched by using non-local numbers, in order to determine the non-satisfied length of it, naturally and straightforwardly.

This achievement can't be deduced by the classical reasoning, as long as it ignores non-local numbers.

The distinction among locality and non-locality as fundamental properties of a given mathematical framework, enables further understanding of Entropy, which is essential to further development of living creatures like us.
 
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Continue to jump all over the place as you see fit, but it changes nothing: Your conclusions still do not follow from your clumsy definitions.


Is a 40-unit line segment a non-composed object?
 
jsfisher said:
Continue to jump all over the place as you see fit, but it changes nothing: Your conclusions still do not follow from your clumsy definitions.


Is a 40-unit line segment a non-composed object?
Click to expand...
The 1-dimesional object with length 40 is non-composed.

Your degenerate local-only reasoning still do not follow my posts on this subject.
 
doronshadmi said:
The 1-dimesional object with length 40 is non-composed.
Click to expand...

...and then a 20-unit line segment would be a non-composed object. A 20-unit line segment could be situated completely "at" a 40-unit line segment. That would make the 20-unit line segment "local" to the 40-unit line segment.

Do you want to make any last minute changes to your definition, Doronshadmi?
 
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