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10th November 2014, 07:36 AM  #1 
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Deeper than primes  Continuation 2
N folded line segments does not mean that one of the folded line segments has N subsegments. For example, in the case of Koch Fractal the formula is (X/4J)*4J, where j=1 to N, such that if j = N, this is exactly the case that enables to extend (to go beyond) all the cases of finite subsegments, in order to get X in the case of 2*(a+b+c+d+...) (this is exactly N observation). This is not the case if X is observed from R, exactly because N extension < lR, and we need R extension in order to get X. Please look again very carefully at http://www.internationalskeptics.com...postcount=4298. 
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10th November 2014, 07:50 AM  #2 
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10th November 2014, 08:35 AM  #3 
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If you read all of
Originally Posted by doronshadmi
jsfisher, mathematical expressions like n = 1 to ∞ are used, isn't it? I simply refine ∞ by distinguish between N and R. 
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10th November 2014, 09:10 AM  #4 
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You overrate your power of expression with clarity.
Be that as it may... You have a (countably infinite) sequence of values that has a limit of a value. The cardinality of the set of reals is irrelevant to this. On the other hand, if you want to take a line segment view of the process, you have a (countably infinite) sequence of line segments that collectively span a line segment. All of the line segments involved have the same "number" of points, but, again, the cardinality of the continuum is not relevant. Instead, rather than staying consistent, you switch midway to conflate the two and view the resulting confusion as revelation. 
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10th November 2014, 09:58 AM  #5 
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It is relevant.
You arbitrarily force N as the only possible option to obverse the realline. I do not switch midway, on the contrary, I show two different cases that depend of two different observations, as follows: 1) By using N observation of the realline 2*(a+b+c+d+...)=X. 2) By using R observation of the realline 2*(a+b+c+d+...)<X. 
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10th November 2014, 10:07 AM  #6 
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10th November 2014, 10:33 AM  #7 
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Series 2*(a+b+c+d+...) is based on the convergent sequence <a,b,c,d,...> of N values.
2*(a+b+c+d+...)=X by define X as the limit of 2*(a+b+c+d+...), as follows: N+1 = N (where this +1 is exactly the way that is used to define X as the limit of 2*(a+b+c+d+...)). By using the fact that N+1 = N you can conclude that 2*(a+b+c+d+...)=X. But this little trick does not work from R observation of the realline simply because N+1 = N < R. 
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10th November 2014, 12:35 PM  #8 
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10th November 2014, 01:22 PM  #9 
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10th November 2014, 01:49 PM  #10 
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Ok, now let's go beyond the realline in order to deal with the tower of power line.
It goes like this: Between any two natural numbers along the tower of power line, there are N rational numbers. Between any two rational numbers along the tower of power line, there are R irrational numbers. Between any two irrational numbers along the tower of power line, there are P(R)_numbers. Between any two P(R)_numbers along the tower of power line, there are P(P(R))_numbers. ... etc. ... ad infinitum, where the inaccessible limit of the tower of power line is simply the noncomposed 1dimesional space. 
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10th November 2014, 01:51 PM  #11 
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10th November 2014, 02:09 PM  #12 
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10th November 2014, 02:19 PM  #13 
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10th November 2014, 09:16 PM  #14 
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11th November 2014, 05:10 AM  #15 
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11th November 2014, 05:18 AM  #16 
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11th November 2014, 06:34 AM  #17 
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11th November 2014, 06:41 AM  #18 
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11th November 2014, 06:53 AM  #19 
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If those posts addressed my question, I won't need to repeatedly ask it. The question was:
Meanwhile, back to where we were not discussing the real line at all, but the valuation of a convergent series, how is the cardinality of the real numbers relevant? And for the sake of context and example, the series represented by 0.999... is the reference. 
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11th November 2014, 07:59 AM  #20 
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http://www.internationalskeptics.com...postcount=4282 and http://www.internationalskeptics.com...postcount=4298 deal with the same reasoning, which is N and R observations of the realline.
This time please do not ignore the details of http://www.internationalskeptics.com...37&postcount=7 and http://www.internationalskeptics.com...59&postcount=9. In other words, there is no It is up to you to decide if you wish to continue the discussion on N and R observations of the realline. (http://www.internationalskeptics.com...postcount=4312 goes beyond the realline). 
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11th November 2014, 08:13 AM  #21 
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11th November 2014, 08:25 AM  #22 
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As long as notion is impossible because of partial usage of one's brain skills, new glasses will not help.  If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) 

11th November 2014, 08:36 AM  #23 
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As long as notion is impossible because of partial usage of one's brain skills, new glasses will not help.  If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) 

11th November 2014, 09:36 AM  #24 
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11th November 2014, 10:22 AM  #25 
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Huh? How else would you note down an enumeration from 1 to ∞?
And what has an enumeration to do with the concept of infinity (notice, no capital I, it is not a deity or some shady wooconcept). Infinity is really, really simple; it has no end; 'In' as in 'the opposite of' and 'fin' as in 'end'. Literally it means endless. How hard can this be? 
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11th November 2014, 01:08 PM  #26 
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Yes, the irony of avoiding http://www.internationalskeptics.com...7&postcount=20 by you, as clearly shown by your nonreply to it in http://www.internationalskeptics.com...7&postcount=21.

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11th November 2014, 01:14 PM  #27 
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Doron, you have yet to show how the valuation of 0.999... invokes the continuum.

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11th November 2014, 01:19 PM  #28 
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As long as notion is impossible because of partial usage of one's brain skills, new glasses will not help.  If a tree falls in the forest, and no one’s there to see it, the tree and ground still measure each other. ( http://www.askamathematician.com ) 

11th November 2014, 01:52 PM  #29 
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12th November 2014, 01:14 AM  #30 
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You still exclude yourself as an essential factor of R observation of the realline.
Without your R observation of the realline, you simply unable to know why 0.999... (which is an N thing) < 1 by 0.000...1 (the needed knowledge about 0.000...1 is found in http://www.internationalskeptics.com...postcount=4282). This is exactly the hint for you. 
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12th November 2014, 03:08 AM  #31 
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Awesome, Doron's ageold "I know what I am, but what are you? I am from rubber, you are from glue, anything you say bounces off me and sticks to you!" Kindergarten tactics.
If he does not answer I will start reporting those and the previous posts for breach of contract; he is not furthering the discussion; he just wants to win the fight. 
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12th November 2014, 06:17 AM  #32 
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12th November 2014, 08:04 AM  #33 
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14th November 2014, 02:22 AM  #34 
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Let's correct what I wrote in http://www.internationalskeptics.com...postcount=4275.
The right one is this:  By using R size observation: 0.999..._{10} < 1 by 0.000...1_{10} 0.888..._{9} < 1 by 0.000...1_{9} The difference between 0.000...1_{10} and 0.000...1_{9} is given by direct proportionality, according to the following formula: abs( (1/9)/(1/10) ) (the result can't be expressed by any particular base, because this ratio is done between bases). The general formula for all n>1 natural numbers is: base j = 2 to n base k = 2 to n abs( (1/(base j)) / (1/(base k)) ), such that j ≤ k. 
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14th November 2014, 12:35 PM  #35 
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And what is the use of this? Besides it being convoluted and based on the *WRONG*ful notion of there being a finite digit in an infinite series.
Also, this formula yields a rather weird result when j equals k... namely 1. So the difference between two exact same numbers in the exact same base is 1? If that is not proof of Doron's inability to do mathematics, then I do not know what more is needed. 
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14th November 2014, 02:26 PM  #36 
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The proportionality of a given value to itself is 1.
abs( (1/(base j)) / (1/(base k)) ), such that j ≤ k calculates the value of proportionality within (0,1], such that a value < 1 means less self proportionality that can be translated into greater difference between two given values by the following formula: n is some natural number > 1 base j = 2 to n base k = 2 to n 1/abs( (1/(base j)) / (1/(base k)) ), such that j ≤ k (the result can't be expressed by any particular base, because this ratio is done between bases). 
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14th November 2014, 03:43 PM  #37 
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Again, you are not supposed to be reading my posts; you are ignoring me. Keep this up and you'll be reported for categorically breaking the agreement.
Now, if you mean ratio, then do not use the word difference. Difference means the distance along a line that two values are apart. Please be more rigorous in your use of language, it is so hobbyish if you just 'do something'. Furthermore, if the result can not be expressed in any particular base, then you can not define And again, you use the word difference where you want to use ratio. Shoddy work that promises not much good for the rest of the dreamcastle that is being built on this... 
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14th November 2014, 04:42 PM  #38 
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Difference between values is not necessarily distance in terms of metric space.
For example, the different proportion between two values can be translated into greater values by the following formula: n is some natural number > 1 base j = 2 to n base k = 2 to n 1/abs( (1/(base j)) / (1/(base k)) ), such that j ≤ k (the result can't be expressed by any particular base, because this ratio is done between bases, so the formula itself is the result). 
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15th November 2014, 02:53 AM  #39 
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Simple counter example:
1/9 = 0.111... 2/9 = 0.222... 3/9 = 0.333... ... 9/9 = 0.999... = 1 Another approach: 9 * 1/9 = 9/9 = 1 9 * 0.111... = 0.999... = 1 Once more, with more rigor (I've tried to make each step as explicit and obvious as possible): A similar proof exists for 0.888..._{9}, as well as all other fixed point decimals. Every fixed point decimal in any base has an infinite decimal infinite decimal representation in that base: 0.12_{10} = 0.11999999..._{10} 0.25_{10} = 0.2499999..._{10} 0.345_{9} = 0.3448888888..._{9} 100111.110101_{2} = 100111.1101001111111111..._{2} 1.0_{9} = 0.88888..._{9} To put it another way, every closed interval [n,m] has exactly zero length when n is fixed point decimal and m is it's infinite decimal expansion. I know you have an intuitive belief that there must be some infinitesimal quanity between 0.999... and 1, but intuition is no substitute for a mathematical proof. How would you construct that quantity, and how do you show it is greater than 0? Can you show something more rigorous than an informal "size observation"?
Quote:

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15th November 2014, 03:19 AM  #40 
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Hey Dessi,
Your reply is right if you are using N observation of the realline. I use R observation of the realline, as given in http://www.internationalskeptics.com...postcount=4282, where the correction of the example there is given in http://www.internationalskeptics.com...2&postcount=34. I use N<R, which is based on a rigorous mathematical proof.  Please also read very carefully all of what is written in http://www.internationalskeptics.com...postcount=4298, http://www.internationalskeptics.com...64&postcount=1 (some correction of this post: "X/4J)*4J, where j=1 to N" has to be "X/4^{J})*4^{J}, where j=1 to N, such that N is not a value along the realline") , http://www.internationalskeptics.com...41&postcount=3 and http://www.internationalskeptics.com...37&postcount=7, if you wish to reply to them. Thank you. 
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