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19th January 2019, 02:22 PM  #3281 
Penultimate Amazing
Join Date: Mar 2008
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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. 

29th January 2019, 04:36 AM  #3282 
Penultimate Amazing
Join Date: Mar 2008
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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 zigzag (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 zigzag 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 zigzag 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. 

29th January 2019, 07:21 AM  #3283 
Penultimate Amazing
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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 nonomitted 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. 

29th January 2019, 07:30 PM  #3284 
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error

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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 
Penultimate Amazing
Join Date: Mar 2008
Posts: 12,887

The standard notion of set (according to Prof. Melvin Randall Holmes):
Quote:
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. 
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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. 

2nd February 2019, 11:52 PM  #3286 
Penultimate Amazing
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By going beyond the notion of collection (which is a composed thing) the noncomposed is defined by noncomposed 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 noncomposed, one enables to understand why a collection with endless members is not actual infinity, simply because it is inaccessible to YESthing (that has cardinality ∞). 
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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. 

15th March 2019, 01:42 AM  #3287 
Penultimate Amazing
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Math Over Matrix (MOM) vs Math Under Matrix (MUM)
Please very carefully observe Prof. Edward Frenkel's YT video on vectors https://www.youtube.com/watch?v=PFkZGpN4wmM .
The essence of his notion is given from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video, where he introduces the notion of Math Over Matrix, which is actually our ability to deduce also beyond the notion of collections (the mug is not a collection of its projections). Math Over Matrix or MOM axiomatic framework is given in http://www.internationalskeptics.com...postcount=3095 , http://www.internationalskeptics.com...postcount=3108 and http://www.internationalskeptics.com...postcount=3110 and it is done by using visual_spatial AND verbal_symbolic reasoning.  Math Under Matrix or MUM is done by using only verbal_symbolic reasoning. By MUM, for example, 0.999...[base 10] = 1, and a person named Chirs Seib ( please look at the discussions in https://www.youtube.com/watch?v=SDtFBSjNmm0&t=3s ) provided a generalization for any base > 1, as follows: First we observe that the base value is always greater by 1 from the digits that are used in the numbers of the form B.BBB... (where B is any digit > 0), for example: If B = 1, then the base value is 2. If B = 2, then the base value is 3. If B = 3, then the base value is 4. ... If B = 9, then the base value is 10. etc. ... Here is @Chris Seib general form for any base > 1: (B+1) * 0.BBB... = B.BBB... B * 0.BBB... + 0.BBB...= B + 0.BBB... B * 0.BBB... = B 0.BBB... = 1  Let B = 9 (without loss of generality) and in that case the base value is 9+1=10 In that case we have the following steps: 10 * 0.999... = 9.999... (9+1) * 0.999... = 9.999... 9 * 0.999... + 0.999...= 9 + 0.999... 9 * 0.999... = 9 0.999... = 1 Let's do it in "slow motion" (as suggested by @logic892173): 10 * 0.999... = 9.999... (9+1)*0.999... = 9.999... 9 * 0.999... + 1*0.999... = 9.999... 9 * 0.999... + 0.999... = 9.999... (as @logic892173 wrote "the distributive property say that (a+b)*c = a*c + b*c for any real numbers a,b,c") 9 * 0.999... + 0.999...= 9 + 0.999... 9 * 0.999... = 9 (9*0.999...)/9 = 9/9 1*0.999... = 9/9 0.999... = 1 Alternatively (9*0.999...)/0.999... = 9/0.999... 9*1 = 9/0.999... 9 = 9/0.999... 9/9 = (9/0.999...)/9 1= (9/0.999...)/9 So the general form as given by @Chris Seib holds perfectly (or so it seems at first glance as long as one is unaware of MOM and MUM difference). I admit, I am doing a lot of mistakes during my work, and the last one was my nonsensical treatment about (5*2)=10 and 9*0.999...=9 (as I did in https://www.youtube.com/watch?v=SDtFBSjNmm0&t=3s). So let's do it very carefully in order to avoid (as much as possible) nonsensical treatments about 0.999... First, here is again the relevant part of my argument to @Mathologer about 0.999... : "@Mathologer at 12:16 you subtract M=9+9/10+9/100+9/1000+... from 10M=90+9+9/10+9/100+9/1000+... and you are left with 9M=90. But by doing so you simply eliminate M that is the result of endless added values that all of them > 0 (which means that there is always some value > 0 that permanently prevents us from actually reaching (to be equal) a given limit value. So by your last step ((9M=90)/9=1M=10) the result M=10 has nothing to do with the omitted "tail" (as you call it in 12:16) M=9+9/10+9/100+9/1000+... (they are not the same mathematical object, even if they have the same name (called in this case "M")). In other words, your "slow motion" analysis does not prove that 9+9/10+9/100+9/1000+... = 10." Now, let's carefully observe 9 * 0.999... = 9 as follows: It has to be stressed that every number ≠ 0 that is divided by itself is equal 1, and so is the case about 0.999.../0.999... = 1 So, by this division (9 * 0.999...)/0.999... = 9/0.999... the property of 0.999... (at the left side of the equation) as an endless addition of numbers that every one of them > 0, simply "gets off stage", as seen in the left side of the equation, as follows: (9 * 0.999...)/0.999... = 9*(0.999../0.999...) = 9*1 (the property of 0.999... (at the left side of the equation) as an endless addition of numbers that every one of them > 0, simply "gets off stage") The result of this division is equivalent to the result of subtract M=9+9/10+9/100+9/1000+... from 10M=90+9+9/10+9/100+9/1000+... in @Mathologer's argument (in both cases the property of 0.999... as an endless addition of numbers that every one of them > 0, simply "gets off stage"). So by taking 9 * 0.999... = 9 and dividing both sides by 0.999..., we get 9*1 = 9/0.999... And by 9/9 = (9/0.999...)/9 we get 1 = 1/0.999... exactly because at the previous step we did 0.999../0.999..., which actually eliminates the property of 0.999... as an endless addition of numbers that every one of them > 0. Also please pay attention that by dividing both sides of 9 = 9/0.999... by 9 ( as follows: 9/9 = (9/0.999...)/9 ) we get 1 = 1/0.999... Please very carefully pay attention that 0.999... is not impacted by this division (the division is done only on 9 in both sides of the equation) but since it is compared to a number that is divided by itself (where the result can't be but 1) we have lost the ability to distinguish between a fixed number like 1 and a nonfixed number like 0.999... as an endless addition of numbers that every one of them > 0, which is fundamentally different than 1 (if it is defined by using also visual_spatial reasoning, which is something that traditional mathematicians don't do about arithmetic). Let's return once again to 9 * 0.999... = 9 and divide its both sides by 9 as follows: (9*0.999...)/9 = 9/9 9/9*0.999... = 9/9 (every number ≠ 0 that is divided by itself is equal 1) and we get 0.999... = 1 Also in this case please very carefully pay attention that 0.999... is not impacted by this division (the division is done only on 9 in both sides of the equation) but since it is compared to a number that is divided by itself (where the result can't be but 1), we have lost the ability to distinguish between a fixed number like 1 and a nonfixed number like 0.999... as an endless addition of numbers that every one of them > 0, which is fundamentally different than 1 (if it is defined by using also visual_spatial reasoning, which is something that traditional mathematicians don't do about arithmetic).  Both 0.999...[base 10] = 0.9+0.09+0.009+0.0009+... or 2(a+b+c+d+...) (please observe ) are known as forms of convergent series, so the discussion generally argues about such forms, and this is exactly how fruitful mathematical discussion is done, by going beyond some particular form (0.999...[base 10] in this case).  Let's observe 2(a+b+c+d+...) it terms of MOM, which is a deduction that is done by by using visual_spatial AND verbal_symbolic reasoning, as follows: During your observation of https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg please be focused on the following: 1) There are aleph0 bent 1dim orange forms that all of them have length 1. 2) These aleph0 bent 1dim orange forms construct 2(a+b+c+d+...) along the straight 1dim orange form, which has length 1. 3) 2(a+b+c+d+...) = the length of the straight 1dim orange form iff there is at least one bent 1dim orange form (which is one of the aleph0 constructors of 2(a+b+c+d+...) along the straight 1dim orange form), that its length = 0. 4) Since (3) does not hold (aleph0 bent 1dim orange forms are inaccessible to the point at the bottom of the diagram (length=0)) 2(a+b+c+d+...) < the length of the straight 1dim orange form. 5) By (4) 2(a+b+c+d+...) does not have a sum exactly because of this inaccessibility. Again, please observe https://farm5.staticflickr.com/4015/...f5b36c0f_o.jpg and carefully follow all of these 5 steps during the observation (by all I mean that do not stop before all of the 5 steps are done During the observation). Please let me know what you have discovered. Thank you. 
__________________
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. 

15th March 2019, 01:56 PM  #3288 
Penultimate Amazing
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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 noncomposed by nature (addressed as noncomposed ________).
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 symboliconly 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. 

15th March 2019, 03:52 PM  #3289 
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15th March 2019, 08:53 PM  #3290 
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Please define 1dim.

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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 
Penultimate Amazing
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A non fixed number is a value that does not have a sum.
For example 0.999...[base 10] is a nonfixed 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 nonfixed number) is already given in http://www.internationalskeptics.com...postcount=3288 . 
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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, 09:11 AM  #3292 
Nitpicking dilettante
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Didn't you just show 0.999... = 1 ?

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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 
Penultimate Amazing
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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 
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__________________
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. 

17th March 2019, 01:26 AM  #3295 
Penultimate Amazing
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login892173: The symbol "<" represent an order relation. It is usually defined in the real numbers but if that sum has no value then it is not a real number.
0.999...[base 10] < 1 by 0.000...1[base 10], where ...1 at 0.000...1 indicates the inaccessibility of potential infinity (infinity that is based on the notion of collections) to actual infinity (infinity that is beyond the notion of collections, and therefore it is a noncomposed whole) exactly as axiomatically given in http://www.internationalskeptics.com...postcount=3095 , http://www.internationalskeptics.com...postcount=3108 and http://www.internationalskeptics.com...postcount=3110. Moreover, the notion of existence that goes beyond the notion of collections (what I define as actual infinity) is very simply addressed in Prof. Edward Frenkel's video as observed from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video. login892173: In traditional Math infinite sums are defined to have a value and in this case 0.(9) can be defined to be the value of the infinite sum of the terms 9/10^n for all natural numbers n. Since your interpretation of your drawings gives you a different definition, the answer you arrive with your drawings is irrelevant because it represent different objects. What you call traditional Math is a Math Under Matrix framework (MUM) exactly because it is fundamentally values things by the notion of collections. I use Math Over Matrix framework (MOM) that fundamentally values things by also going beyond the notion of collections. MOM enables to use potential infinity (the composed existence of infinite collections) and actual infinity (the noncomposed existence beyond finite or infinite collections) in one framework. That is also over the matrix, is aware of the matrix. That is under the matrix, is unaware of the matrix. In order to be also over the matrix, one uses visual_spatial AND verbal_symbolic reasoning. More details are given in http://www.internationalskeptics.com...postcount=3287 and http://www.internationalskeptics.com...postcount=3291. 
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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. 

17th March 2019, 03:33 AM  #3296 
Penultimate Amazing
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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 1dim orange forms with length=1 that construct 2(a+b+c+d+...)) is the noncomposed that is beyond the composed (actual infinity is inaccessible to every infinite collection). 
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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. 

17th March 2019, 06:34 AM  #3297 
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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. 

17th March 2019, 01:31 PM  #3298 
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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. 
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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. 

17th March 2019, 01:55 PM  #3299 
Penultimate Amazing
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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) ... Code:
1 2 3 ... ↓ ↓ ↓ 0.9 + 0.09 + 0.009 + ... 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 + ... 
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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. 

17th March 2019, 09:53 PM  #3300 
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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. 

17th March 2019, 10:01 PM  #3301 
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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. 

19th March 2019, 12:06 AM  #3302 
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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. 

19th March 2019, 04:13 AM  #3303 
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Post number?

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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. 

19th March 2019, 07:34 AM  #3304 
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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. 

19th March 2019, 07:38 AM  #3305 
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You are claiming something. Please support your claim..

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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. 

19th March 2019, 08:41 AM  #3306 
Nitpicking dilettante
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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 

19th March 2019, 09:38 AM  #3307 
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You take a part of it, and therefore get wrong conclusions about it.
Please this time observe all of it, before you conclude anything about it. Furthermore, please observe also my other posts after it, which provide more details about it. 
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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. 

19th March 2019, 11:01 AM  #3308 
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0.999... isn't an endless addition. It's a number.
Or maybe you believe that because the character sequence "0.999..." looks different from "1", they can't represent the same number? Is that the essence of "visual_spatial reasoning"? Nobody here agrees with your ideas. Maybe you should spend some time thinking about why. 
19th March 2019, 11:34 AM  #3309 
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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 

20th March 2019, 12:01 AM  #3310 
Penultimate Amazing
Join Date: Mar 2008
Posts: 12,887

This is a good question.
If time is involved, then YES, 0.999...[base 10] is an endless process of addition, which is less than 1. If time is not involved, then NO, 0.999...[base 10] is the inaccessibility of the composed (the potential infinity of the collection of infinitely many finite (and I would say fixed) numbers) to the noncomposed existence of ______ (which is actualinfinity that is AXIOMATICALLY beyond the composed). So it is up to us, we can choose to consider time as a factor of our mathematical framework, OR NOT (which is something that zooterkin does not grasp, yet). 0.999...[base 10] = 0.9 + 0.09 + 0.009 + ...[base 10] is a nonfixed number that is inaccessible to 1 that is a fixed number at the edge of 0_______1 (where _______ is noncomposed (is it AXIOMATICALLY actual infinity)). More details are already given in http://www.internationalskeptics.com...postcount=3295. The essence is the notion that is based on both visual_spatial AND verbal_symbolic reasoning, which AXIOMATICALLY enables one to actually know the difference between potential infinity (infinity in terms of the composed) and actual infinity (infinity in terms of the noncomposed) in one mathematical framework, such that potential infinity is logically inaccessible to actual infinity, exactly because potential infinity is AXIOMATICALLY infinitely weaker than actual infinity. By understand this inaccessibility, 0.9 + 0.09 + 0.009 + ... is inaccessible to number 1 at 0_________1, exactly because ________ (the noncomposed (defined as actual infinity)) is AXIOMATICALLY beyond the composed (defined in terms of collections). By ACTUALLY USING visual_spatial AND verbal_symbolic reasoning, one gets the following hierarchy of existence: 1) Actual infinity (the noncomposed) 2) Finite (the finitely composed that is finitely weaker than the noncomposed and therefore can be added up to a given value (for example 1, that is defined at the edge of 0______1) 3)Potential infinity (the infinitely composed that is infinitely weaker than the noncomposed and therefore can't be added up to a given value (for example 1, that is defined at the edge of 0______1) Furthermore, my axiomatic framework is supported by Prof. Edward Frenkel as clearly observed from https://youtu.be/PFkZGpN4wmM?t=697 until the end of the video (the mug (the noncomposed or actual infinity) is not the composed (it is not the collection of its projections). More details are given in http://www.internationalskeptics.com...postcount=3095. 
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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. 

20th March 2019, 05:30 PM  #3311 
Graduate Poster
Join Date: Nov 2006
Posts: 1,938

Again, more hand waving that does exactly nothing.
0.99999... is not the sum of an infinite series. Pi is infinite, but it is not (3.0 + 0.1+ 0.04 + 0.001 + 0.0005 + 0.00009 + ...) 
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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. 

20th March 2019, 07:08 PM  #3312 
Philosopher
Join Date: Aug 2003
Location: Detroit
Posts: 5,405

Doronshadmi, look into palindromic numbers and their sums. The key lies there. Trust me.

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Fill the seats of justice with good men; not so absolute in goodness as to forget what human frailty is.  Thomas Jefferson What region of the earth is not filled with our calamities?  Virgil 

22nd March 2019, 03:10 PM  #3313 
Penultimate Amazing
Join Date: Mar 2008
Posts: 12,887


__________________
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. 

22nd March 2019, 04:02 PM  #3314 
I say nay!
Join Date: Aug 2010
Location: Long Island
Posts: 3,601


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I am 100% confident all psychics and mediums are frauds. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "0111100101111001011010000111011001110110001101100 0110101001101100" Said the robot gleefully as he went on his rampage. 

Yesterday, 08:43 AM  #3315 
Philosopher
Join Date: Aug 2003
Location: Detroit
Posts: 5,405

I capitalize but not symbolic

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Fill the seats of justice with good men; not so absolute in goodness as to forget what human frailty is.  Thomas Jefferson What region of the earth is not filled with our calamities?  Virgil 

Yesterday, 02:39 PM  #3316 
Penultimate Amazing
Join Date: Mar 2008
Posts: 12,887


__________________
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. 

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