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 International Skeptics Forum Continuation Deeper than primes - Continuation 2

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 19th January 2019, 02:22 PM #3281 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Wholeness is not necessarily Comleteness Wholeness is not necessarily Completeness, as seen in http://www.internationalskeptics.com...postcount=2798 exactly because infinitely many things are infinitely weaker that actual infinity (as seen in http://www.internationalskeptics.com...postcount=3095). In order to deal with such notions, philosophy and mathematics are inseparable of each other (http://www.internationalskeptics.com...postcount=3280). __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 19th January 2019 at 02:46 PM.
 29th January 2019, 04:36 AM #3282 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Please look at the following diagram: It was known as "2X=X√2 paradox" (This is an old "problem" that was known at least to Leibniz and probably to the Greeks). Actually, this is not a paradox at all since no integer is an irrational number, and a straightforward way to show it, is by X=1, that is, 2>√2. By observing the top of the attached diagram, one finds the convergent series a+b+c+d+... 1) Please pay attention that this series is rigorously defined by the intersections of the black straight lines (which go through the peaks of the zig-zag (black, red, green, magenta, blue, cyan) lines with constant length 2X) with each side of the square. 2) It means that the mathematical fact that 2X>X√2, is inseparable of the mathematical fact that 2X>2(a+b+c+d+...). Let X (one side of the square) = 1 In that case (a+b+c+d+...) is actually (1/2+1/4+1/8+1/16...). By (2) 2(1)>2(1/2+1/4+1/8+1/16...), which can be reduced into 1>1/2+1/4+1/8+1/16... It has to be stressed that no partial sums like a, a+b, a+b+c, ... are involved in this argument, but not less than the series a+b+c+d+... If one does not agree with the argument above, one has to prove (according to the considered diagram) that series a+b+c+d+... is not defined by the zig-zag lines (where, again, no partial sums like a, a+b, a+b+c, ... are involved in such proof). Moreover, if one proves it, one also demonstrates why visualization is insufficient for rigorous mathematical results. I am fully aware that what is called "not a summation in the usual sense" means a+b+c+d+... ≤ X, where the semantics (meaning) of ≤ (in the considered case) is "not greater than" X, or "at most" X. Since series a+b+c+d+... is strictly defined by all the zig-zag lines such that 2X is strictly > X√2, series a+b+c+d+... can't be but strictly < X. So I still do not see how ≤ is relevant to the diagram above. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 29th January 2019 at 06:23 AM.
 29th January 2019, 07:21 AM #3283 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 I wish to stress that, for example: S = 1/2+1/4+1/8+1/16... 2S = 1+1/2+1/4+1/8+1/16... 2S - S = 1 - S is not a proof of the considered case because: 1) By omitting S from 2S there is no guarantee that the omitted value (= 1/2+1/4+1/8+1/16...) is equal to the non-omitted value (= 1). 2) The separability between 2>√2 and 1>1/2+1/4+1/8+1/16... has not been proven. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 29th January 2019 at 07:44 AM.
 29th January 2019, 07:30 PM #3284 Little 10 Toes Graduate Poster     Join Date: Nov 2006 Posts: 1,930 error __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 31st January 2019, 08:30 AM #3285 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 The standard notion of set (according to Prof. Melvin Randall Holmes): Quote: A set is a collection determined by its elements. Finite sets are often written {a, b, c} (for example), by listing their elements. Order does not matter and repeated items do not change the intended meaning. The elements of the sets are not parts of the set. The set is not made by conglomerating its elements together. This is a common misunderstanding. To see this it is enough to play with the notation. {x} is not the same object as x: if a set were made up of its elements as parts, this would not make sense. If you don’t believe this, look at {{2, 3}}: this is a set with one element, while its sole element is a set with two elements, so they are different. Another way of seeing it is to notice that a relation of part to whole should be transitive. If a is part of b and b is part of c, then a is part of c. But notice that 2 ∈ {2, 3} and {2, 3} ∈ {{2, 3}}, but 2 is not a member of {{2, 3}} By logically going beyond the notion of collection |{}| is tautology and {||} is contradiction, such that any given collection is ~contradiction AND ~tautology. As about cardinality: {||} = 0 |{}| = ∞ = the cardinality of actual infinity {|...|} = any cardinality > 0 AND < ∞ Some examples: {|{}|} = 1 |{{}}| = ∞ {{||}} = 0 {|{1,2}|} = 1 {{|1,2|}} = 2 {|1,2|} = 2 {{1,{||},2}} = 0 |{{1,{},2}}| = ∞ Nested cardinality examples: |{|{|1,{||},2|}|}| = (((0)3)1)∞ |{|{|1|,{||},2}|}| = (((0)1)1)∞ |{|{|1|,{||},|2|}|}| = (((0)1,1)1)∞ |{|{|1|,|{||}|,|2|}|}| = (((0)1,1,1)1)∞ |{||}| = (0)∞ etc. ... ------------------- As can be seen, the standard notion of collection is a very limited mathematical framework. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 31st January 2019 at 08:50 AM.
 2nd February 2019, 11:52 PM #3286 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 By going beyond the notion of collection (which is a composed thing) the non-composed is defined by non-composed opposite extremes, which are NOthing and YESthing, where the cardinalities (the magnitudes) of them are |{||}| = (0)∞ So the cardinality of any give collection is > 0 AND < ∞, which means that no collection is accessible to that has cardinality 0 (NOthing) or cardinality ∞ (YESthing). By being aware of the composed and the non-composed, one enables to understand why a collection with endless members is not actual infinity, simply because it is inaccessible to YESthing (that has cardinality ∞). __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 3rd February 2019 at 12:11 AM.
 15th March 2019, 01:56 PM #3288 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 What is 0.000...1 by visual_spatial AND verbal_symbolic reasoning? By deduce visually AND symbolically one understand that the ...1 of 0.000...1 simply indicates that any given infinite collection (and in this case the infinitely many 0.9+0.09+0.009+...) is infinitely weaker than actual infinity, which is non-composed by nature (addressed as non-composed ________). So by deduce visually AND symbolically it is easily understood that 0.000...1 symbolically represents the endlessly smaller that can't be the smallest, where again being endlessly smaller is not any particular smaller value, but it is the general inability to be the smallest (there is always _ at the "right side" of _________ that can't be reduced into a point (can't become the smallest, and this is exactly what is given visually AND symbolically in https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg)). Those who deduce only symbolically are closed under the matrix of collections and therefore wrongly deduce actual infinity in terms of collections, and as seen in "0.(9) + 0.(0)1 = 0.(9)1" symbolic gibberish , they are unaware of being under the symbolic-only matrix. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 15th March 2019 at 02:16 PM.
 15th March 2019, 03:52 PM #3289 Hevneren Thinker   Join Date: Jul 2007 Posts: 182 Originally Posted by doronshadmi ... we have lost the ability to distinguish between a fixed number like 1 and a non-fixed number like 0.999... ﻿ I certainly have lost that ability. What is a non-fixed number? Does it move around? Is it greater today than it was yesterday? And why do you think it's a number? A variable could easily pull off all that.
 15th March 2019, 08:53 PM #3290 Little 10 Toes Graduate Poster     Join Date: Nov 2006 Posts: 1,930 Please define 1-dim. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 16th March 2019, 08:51 AM #3291 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Originally Posted by Hevneren I certainly have lost that ability. What is a non-fixed number? Does it move around? Is it greater today than it was yesterday? And why do you think it's a number? A variable could easily pull off all that. A non fixed number is a value that does not have a sum. For example 0.999...[base 10] is a non-fixed number, where 1 is a fixed number. 0.999...[base 10] < 1 exactly by 0.000...1[base 10] (where "exactly" is not necessarily "fixed"). More about 0.000...1[base 10] (which is also a non-fixed number) is already given in http://www.internationalskeptics.com...postcount=3288 . __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; 16th March 2019 at 08:54 AM.
 16th March 2019, 09:11 AM #3292 zooterkin Nitpicking dilettanteDeputy Admin     Join Date: Mar 2007 Location: Berkshire, mostly Posts: 41,938 Didn't you just show 0.999... = 1 ? __________________ The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts.Bertrand Russell Zooterkin is correct Darat Nerd! Hokulele Join the JREF Folders ! Team 13232 Ezekiel 23:20
 16th March 2019, 09:13 PM #3293 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Originally Posted by Little 10 Toes Please define 1-dim. That has length > 0 AND width = 0. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 16th March 2019, 09:14 PM #3294 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Originally Posted by zooterkin Didn't you just show 0.999... = 1 ? No. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video.
 Yesterday, 03:33 AM #3296 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 The actual limit is beyond any infinite collection. Chris Seib: The limit of the "sequence" of the bent orange lines is the vertex of the triangle and is a point. It is NOT a member of the sequence. You are right, the limit of the composed (where the composed in https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg is a collection of infinitely many bent 1-dim orange forms with length=1 that construct 2(a+b+c+d+...)) is the non-composed that is beyond the composed (actual infinity is inaccessible to every infinite collection). __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; Yesterday at 03:48 AM.
 Yesterday, 06:34 AM #3297 Little 10 Toes Graduate Poster     Join Date: Nov 2006 Posts: 1,930 Originally Posted by doronshadmi That has length > 0 AND width = 0. Any reason why you can't say one dimensional? As soon as you "bend" a line segment , you now have a two dimensional object. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 Yesterday, 01:31 PM #3298 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 Originally Posted by Little 10 Toes As soon as you "bend" a line segment , you now have a two dimensional object. Wrong, you have a fractal dimensional object, which is ≈ 1.2618 But in https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg all we care is the length of the orange forms, whether they are straight or bent. __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; Yesterday at 01:34 PM.
 Yesterday, 01:55 PM #3299 doronshadmi Penultimate Amazing     Join Date: Mar 2008 Posts: 12,881 The symbolic illusion of partial sums argument It is argued that 0.999... is not a term of the sequence (0.9, 0.99, 0.999, ...) By carefully observe (0.9, 0.99, 0.999, ...) one easily discovers that Code: ``` 1 ↓ 2 0.9 = 0.9 ↓ 3 0.99 = 0.9 ( + 0.09) ↓ 0.999 = 0.9+0.09 ( + 0.009) ...``` is actually the same as Code: ``` 1 2 3 ... ↓ ↓ ↓ 0.9 + 0.09 + 0.009 + ...``` or in other words, 0.999... is actually embedded in (0.9, 0.99, 0.999, ...) |N| terms. So the partial sums argument (0.9, 0.99, 0.999, ...) of |N| terms provides exactly the same result as given by 0.999... = 0.9 + 0.09 + 0.009 + ... By rejecting this simple fact (by arguing that 0.999... is not a term of the sequence (0.9, 0.99, 0.999, ...)), one actually claims that 0.9 + 0.09 + 0.009 + ... < 0.9 + 0.09 + 0.009 + ... __________________ That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. For more details, please carefully observe Prof. Edward Frenkel's video from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. Last edited by doronshadmi; Yesterday at 02:28 PM.
 Yesterday, 09:53 PM #3300 Little 10 Toes Graduate Poster     Join Date: Nov 2006 Posts: 1,930 Originally Posted by doronshadmi Wrong, you have a fractal dimensional object, which is ≈ 1.2618 But in https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg all we care is the length of the orange forms, whether they are straight or bent. Like most of your posts, this does not make any sense. __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.
 Yesterday, 10:01 PM #3301 Little 10 Toes Graduate Poster     Join Date: Nov 2006 Posts: 1,930 Originally Posted by doronshadmi It is argued that 0.999... is not a term of the sequence (0.9, 0.99, 0.999, ...) Really? Who is arguing this idea? __________________ I'm an "intellectual giant, with access to wilkipedia [sic]" "I believe in some ways; communicating with afterlife is easier than communicating with me." -Tim4848 who said he would no longer post here, twice in fact, but he did.

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