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16th February 2017, 05:37 AM  #2481 
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You claimed that any proof for 2X = 2(a + b + c + d +...) would be "based on symboliconly reasoning". You were wrong.

16th February 2017, 05:46 AM  #2482 
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Clearly given by the diagrams if visual AND symbolic brain skills are used.
Results (mathematical or not) are comprehended by using our brain skills, and this is not my dichotomy, but it is exactly the dichotomy that is deeply involved in your brain, during your mathematical activity. 
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16th February 2017, 06:11 AM  #2483 
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I offer you to use your visual AND symbolic brain skills abut the issue at hand.
In finite terms. Only in case of finite terms. Please simultaneously use your visual AND symbolic brain skills in order to understand the considered diagram, in order to provide the answer to your question. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 06:13 AM  #2484 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 06:17 AM  #2485 
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16th February 2017, 06:22 AM  #2486 
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Doron probaby won't admit this, but he seems to think there's an ongoing, neverending process of adding smaller and smaller line pieces, so the difference will get smaller for each small piece you add. I think this is his fundamental error. He can't see the X line as a whole.

16th February 2017, 06:30 AM  #2487 
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Your fridge "evidence" does not distinguish between infinite addition and finite addition.
Moreover, it artificially separates what actually have in the considered diagrams, exactly because it uses visualonly reasoning. Furthermore, by writing "based on symboliconly reasoning" (seen in the beginning of http://www.internationalskeptics.com...postcount=2471) I am talking about the traditional mathematical stuff about the issue at hand. If you disagree with me then please provide traditional mathematical stuff about the considered diagrams that deduce them by using both visual AND symbolic reasoning. 
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16th February 2017, 06:46 AM  #2488 
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X line is a noncomposed positive thing if taken on its own.
If it is measured by positive subthings along it, then finitely many positive subthings cover it, but do not have its own noncomposed property. If it is measured by ever smaller infinitely many positive subthings along it, then infinitely many positive subthings do not cover it AND do not have its own noncomposed property. Your fundamental mistake is that you take X line as a collection of positive things AND you also do not distinguish between finite collections and infinite collections along the noncomposed X line. X line on its own is a positive noncomposed thing, which is a notion that your collectionoriented reasoning of X, can't comprehend. Also you avoid http://www.internationalskeptics.com...postcount=2487 and http://www.internationalskeptics.com...postcount=2466 and http://www.internationalskeptics.com...postcount=2467. Moreover, you ignored http://www.internationalskeptics.com...postcount=2465 (and what is written there about Archimedean property (which is definitely not used in my framework)). 
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16th February 2017, 07:09 AM  #2489 
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I could easiy do that, but I have already tried to explain this to you using visual, symbolic, AND combined lines of thought. You just keep rejecting whatever I say. It's your turn to prove your stuff now, not just repeating you false claims. You are totally out of line with mathematics here, so the burden of proof is upon you.

16th February 2017, 07:17 AM  #2490 
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Rubbish. I take X as a line of some length, AND I know the sum of an infinite geometric series. Collections don't enter into it.
It's in fact you that don't seem to get this. Link spamming to you own posts won't get you anywhere. You haven't explained or proved anything at all in your previous posts, so why link to them? If you have some evidence, please just provide it. 
16th February 2017, 07:21 AM  #2491 
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16th February 2017, 07:30 AM  #2492 
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Please show me an infinite geometric series that is not a collection of infinitely many things.
On the contrary, you actually have no clue what is actually X line as a noncomposed thing of its own, which is independent of how we measure it (you still do not comprehend what is written at the beginning of http://www.internationalskeptics.com...postcount=2488). EDIT: Moreover, please provide a traditional mathematical stuff which according to it X line is a noncomposed thing. You ignore the links in those links (which are not my works), exactly because they do not fit to your reasoning. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 07:31 AM  #2493 
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16th February 2017, 07:34 AM  #2494 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 07:58 AM  #2495 
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Exactly. You offer no proof, or even evidence. That's what I said and youseem to confirm.
Are you saying the sum of infinitely many numbers can not have a specific value? Why don't *you* give me the answer? Symbolic tells me the sum exists, and visual tells me the sum exists. Why should that change if I use symbolic AND visual skils? Take some length X. Make it into 2 halves. Call one of the halves a and put it aside. Take the remaining part and make it into two halves. Call one of the halves b and put it aside. Take the remaining part and make it into two halves. Call one of the halves c and put it aside. Repeat infinitely many times (inventing new letters as you go). At no point in the process do I throw anything away, so the sum of the infinitely many bits I end up with must be X. You can visualize the process or put it into symbols or both. The sum will always be X. 
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16th February 2017, 10:34 AM  #2496 
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Once again you do not use your visual AND symbolic brain skills in order to realize that in the considered diagram the fact that 2X>X√2 is inseparable of the fact that 2X>2(a+b+d+d+...). The diagram is the proof of this inseparability only if you are actually simultaneously using both your visual AND symbolic brain skills during its observation.
What I say is that there is no sum to the added positive values in the considered diagram. Because the right answer about the considered diagram is deeply related of how *you* are actually simultaneously using both your visual AND symbolic brain skills during the considered diagram observation. Because this is the whole point, *your* brain can't comprehend the diagram unless *you* simultaneously observe it by using *your* visual AND symbolic brain skills. As long as *you* search for a string of symbols that is observed by *you* as a mathematical proof about the considered diagram, *you* are using *your* symboliconly brain skills, which actually prevent the actual understanding of the considered diagram. Look how *you* actually observe X separately of how it is actually visually AND symbolically defined in the following diagram: FACT 1: No infinitely many staircases with constant value 2X are equal to X√2 (written as 2X>X√2). FACT 2: a+b+c+d+... is the result of the intersections of the diagonal black lines on the peaks of the infinitely many staircases, with the 2X sides of the diagram. FACT 3: The interactions along the 2X sides are inseparable of FACT 1. FACT 4: By FACT 3, one realizes that no infinitely many 2(a+b+c+d+...) are equal to 2X ( written as 2X>2(a+b+c+d+...) ). FACT 5: No infinitely many 2(a+b+c+d+...) have a fixed sum, exactly because 2X>X√2 AND 2X>2(a+b+c+d+...) are inseparable in the considered diagram. FACT 6: FACTS 1 to 5 are known only if one actually simultaneously using both his\her visual AND symbolic brain skills during his\her observation of the considered diagram. 
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16th February 2017, 11:06 AM  #2497 
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True. Nobody disagrees.
OK. What do you mean by inseparable? This isn't clear. Maybe "one" does, but then "one" is wrong. This has been expained to you many times. False. The sum is 2X. It doesn't matter what skills were used when the results are wrong. I think you may have observed that the black diagonals approach length X√2 as the staircase steps grow smaller, and it may look like some paradox that the staircase has constant length 2X while it looks more and more like a straight line as the steps get smaller. Geometry is a fascinating subject, but your answers are still wrong. Now try to disprove the following (it should be easy if you are right): S = 1/2 + 1/4 + 1/8 + 1/16 + ... 2S = 1 + 1/2 + 1/4 + 1/8 + 1/16 ... 2SS= 1 + 1/2 + 1/4 + 1/8 + 1/16 ...  1/2  1/4  1/8  1/16 + ... S=1 Yes, this is symbolic only, but since you master both kinds of reasoning so superbly, it can't be too difficult. 
16th February 2017, 11:15 AM  #2498 
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http://www.internationalskeptics.com...postcount=2496 simply evolved beyond the artificial limitations of *your* symboliconly  visualonly dichotomy.
There is no paradox of any kind here, and exactly because there is not paradox FACTS 1 to 6 hold. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 11:21 AM  #2499 
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16th February 2017, 02:36 PM  #2500 
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It is clear as a noon sun.
No infinitely many staircases are "settled down" into X√2, and since 2(a+b+c+d+...) is the result of the intersections of the diagonal black lines on the peaks of these infinitely many staircases with the 2X sides of the diagram, 2(a+b+c+d+...) can't be "added up" into 2X. 
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16th February 2017, 02:48 PM  #2501 
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Exactly as MetalPig, you observe it separately of the considered diagram, and this is the bast of what your symboliconly  visualonly dichotomous reasoning actually achieves.
So the answer is: you have no proof whatsoever. Still in deep sleep. Still in deep freeze. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

16th February 2017, 05:32 PM  #2502 
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That doesn't make it wrong. The proof stands. Mathematical rigor does not yield to your misinterpretation of simple diagrams nor to your selfproclaimed superior reasoning methods.
The mathematical fact that 1/2 + 1/4 + 1/8 + ... is 1 follows directly from definitions; your insistence otherwise has no impact. Mathematics doesn't care if you don't understand. 
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17th February 2017, 12:14 AM  #2503 
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Nobody disputes this. 2 > √2 , we know.
Maybe you can't add them up, but it can be proven symbolically, and it's visually obvious from your diagram that they add up to 2X. Somehow doing it "symbolically and visually" prevents you from getting to the correct answer. Sad. 
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17th February 2017, 04:57 AM  #2504 
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jsfisher, MetalPig and Hevneren,
http://www.internationalskeptics.com...postcount=2500 is exactly the right result about the considered diagram. No reasoning that is based on the artificial dichotomy between *your* natural abilities to combine *your* visual AND symbolic brain skills, is going to change that right result. Moreover, ignoring http://www.internationalskeptics.com...postcount=2466, http://www.internationalskeptics.com...postcount=2467 and http://www.internationalskeptics.com...postcount=2465 (including the rejection of the Archimedean property) actually put you in an obsolete state with respect to the actual fundamental developments of Maths that are deeply rooted in researches of the human brain. Now days mathematics is an aggregation of frameworks that even contradict each other, exactly because of the lack of Unity consciousness among human beings. Mathematics, together with more scientifically developed methods, is going to play a main factor in developing Unity consciousness among human beings, where drafts in this direction are seen in http://www.internationalskeptics.com...postcount=2342 and http://www.internationalskeptics.com...postcount=2438. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 06:02 AM  #2505 
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Oh no, I'm obsolete. Still not looking forward to the day when all humans have Doron's consciousness

17th February 2017, 09:24 AM  #2506 
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And yet, it isn't. Perhaps if you stopped pretending your diagrams showed what you want to be true and stopped fighting basic definitions in Mathematics, you might actually figure out your diagrams prove nothing while suggesting the opposite of your baseless beliefs.

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17th February 2017, 10:43 AM  #2507 
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17th February 2017, 11:33 AM  #2508 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 11:48 AM  #2509 
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Perhaps if you stopped pretending your symboliconly reasoning showed what you want to be true and stopped forcing it as if it is really basic for actual definitions in Mathematics, you might actually figure out my diagrams prove that 2X>X√2 AND 2X>2(a+b+c+d+...) are inseparable in the considered diagram, despite of your baseless symboliconly beliefs.
The near future of real mathematics is inseparable of human brain research (as briefly given in http://www.internationalskeptics.com...postcount=2504) and the tradition of symboliconly reasoning is going to vanish. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 11:59 AM  #2510 
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17th February 2017, 12:01 PM  #2511 
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17th February 2017, 01:08 PM  #2512 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 01:31 PM  #2513 
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17th February 2017, 03:50 PM  #2514 
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Logical reasoning follows a set of rules based on both visual AND symbolic brain skills in order to draw its conclusions. Got anything like that (for example http://www.internationalskeptics.com...stcount=2504)?

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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 04:01 PM  #2515 
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Typical result of dichotomous visual  symbolic brain skills that is going to vanish simply because real mathematics is done by naturally using both visual AND symbolic brain skills.
A concrete example about the fundamental concept of set, which is based on the natural activity of visual AND symbolic brain skills, is already given in http://www.internationalskeptics.com...postcount=2438. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

17th February 2017, 08:01 PM  #2516 
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This part is correct.
Quote:
Be that as it may, if you do have a set of rules for reasoning (based on whatever you imagine it to be based on), please, tell us all about these rules. I'm sure they will be fascinating. 
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18th February 2017, 02:10 AM  #2517 
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Since you simply unable to realize that your responses are based on your visual AND symbolic brain skills, lets make it more easy for you.
The axiom of mathematics: Given X, no subX is X. In order to really understand this string of symbols both your visual AND symbolic brain skills are simultaneously used, whether you aware of it, or not. So the useful state of mind is to be aware of it during your mathematical work, and this awareness is the mathematical basis for the development of Unity consciousness among human beings. What is already given in http://www.internationalskeptics.com...stcount=2504)? is done by being aware of it during mathematical work, which in turn becomes a useful tool for the development of Unity consciousness among human beings. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

18th February 2017, 07:46 AM  #2518 
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This is not an axiom of Mathematics.
Quote:
Be that as it may, what, I ask again, are your rules for your version of reasoning? They do not correspond to those of mathematical logic, so it would be helpful those playing along at home trying to follow your line of reasoning if they knew what your rules were. 
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18th February 2017, 09:46 AM  #2519 
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I agree with you, because this is The axiom of Mathematics:
Given X, no subX is X. No assertion of any kind, and it is extremely useful by naturally using both our visual AND symbolic brain skills, as already given in http://www.internationalskeptics.com...stcount=2504)? From now on I will reply to you by using The axiom of Mathematics, any attempt from you to ignore it will be a clear sign that you do not really wish to discuss with me about Mathematics and its further development. Now about this axiom, it simply says that that no expressions that may emerge from X, are X, simply because X is noncomposed by definition that is known both visually AND symbolically. 
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As long as Comparison is impossible because of the imbalance of one's mind, 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 ) 

18th February 2017, 10:38 AM  #2520 
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You are reasserting the same falsehood. Got anything to show otherwise?
Quote:
Quote:
Be that as it may, you seem more concerned with the past developments in Mathematics, and that misinterpreting some drawing disproves wellestablished things. 
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