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 January 23rd, 2012, 05:44 AM #21 Senior Member   Joined: Nov 2011 Posts: 599 Thanks: 0 Re: Full Paper - Conjecture 9-14-11 Two more mistakes. I want to emphasize the importance of "NO BLACK HOLES ON EARTH PLEASE!" Shut down those (as far as I can tell) god-foresaken cyclotrons, attempts at alchemy, etc. I ask this by my birthday, 12-20-12, noting the multitude of dooms-day predictions out there for the following day. To CRGreathouse: With some correction for definitions, it should be very apparent that my work (sorry for my lack of humbleness) deserves global attention. Please get to it and let me know! Aside from the breakthroughs in logic and mathematics, the message is clear: People need to stop fighting, start respecting one another, and start working together to solve problems like a lack of resources, over-population, and space exploration. We all have something to learn from one another. On a lighter note, I personally have been going to church because, while nobody is perfect, I am certainly going to start trying to be a better person myself. That is of course my challenge to everyone else also.
January 23rd, 2012, 05:54 AM   #22
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Re: Full Paper - Conjecture 9-14-11

Quote:
 Originally Posted by krausebj0 With some correction for definitions, it should be very apparent that my work (sorry for my lack of humbleness) deserves global attention.
No, that's really not clear. In fact, it's not even apparent that it's worth as much attention as I've given it.

February 11th, 2012, 06:01 PM   #23
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Re: Full Paper - Conjecture 9-14-11

Quote:
Originally Posted by CRGreathouse
Quote:
 Originally Posted by krausebj0 With some correction for definitions, it should be very apparent that my work (sorry for my lack of humbleness) deserves global attention.
No, that's really not clear. In fact, it's not even apparent that it's worth as much attention as I've given it.

Cantor's Theorem (diagonal argument) showed that there were "more" real numbers than natural numbers. This goes against the idea of integration as explained using the Riemann integral. The above paper, Conjecture 9-14-11, undoes Cantor's diagonal argument (if accepted), and restores the validity of integration as explained using the Riemann integral. The importance of the above work therefore seems to be self-apparent. CRGreathouse, in my opinion, should apologize to my friend Brendon for his rude comments and lack of insight.

 February 11th, 2012, 06:24 PM #24 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,168 Thanks: 472 Math Focus: Calculus/ODEs Re: Full Paper - Conjecture 9-14-11 Are you using your friend Brendon's computer to make this post? I ask because you have the same IP address as Brendon, and I certainly hope Brendon has not created a sock puppet account to create the illusion of moral support. How was the statement of [color=#00BF00]CRGreathouse[/color] rude or shortsighted? If you're going to claim that something deserves global attention, the burden of proof is on you, the one making the claim, to demonstrate clearly why this is so. Trust me, you are going to draw much sharper criticism than what [color=#00BF00]CRGreathouse[/color] has given from the worldwide mathematics community at large if things are not clearly defined. Brendon should actually thank [color=#00BF00]CRGreathouse[/color] for taking the time to review a paper that was and apparently continues to be, a work in progress.
 February 12th, 2012, 01:10 PM #25 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Full Paper - Conjecture 9-14-11 Christopher: Are you a mathematician? If so, I think you should provide a more careful analysis of the proof if you think it's worthwhile. If not, I'm not sure on what basis you can rationally claim that the proof is valid.
 February 13th, 2012, 12:00 PM #26 Newbie   Joined: Feb 2012 Posts: 15 Thanks: 0 Re: Full Paper - Conjecture 9-14-11 I'm just a sockpuppet. The set of all infinitely large binary strings is definable. From there, approach each string as follows: g(0.1101...) = { 0.1, 0.11, 0.1101, ... } g(0.1011...) = { 0.1, 0.101, 0.1011, ... } g(0.1111...) = { 0.1, 0.11, 0.111, 0.1111, ... } Doing so results in the set "RI" as defined in the paper. Each element of RI is an infinitely large set of finite binary strings that approach the infinitely large string used to define the element. From here, it should be obvious that the union of all elements in the set RI will equal the set of all finite binary strings. Omit one element of RI from the union, however, and you no longer have the set of all finite binary strings. Omitting one element of RI from the union would leave at least one (or infinitely many) missing finite strings from the resulting union. Therefore, given that the finite binary strings are enumerable (flipping each binary integer accross a decimal point will result in the set of all finite binary strings), so must be the infinitely large ones. That is why the theorem, "... for any element 'j' in RI, 'j' is not a subset of the union of all 'g' in RI such that 'g' is not equal to 'j'" is a disproof of Cantor's theorem if accepted. Not too tough. Again, I am an accountant, not a Math geek. You guys are anal in my book... who cares!! Decimal-shmecimal... A valid disproof of Cantor's diagonal argument spells trouble for Godel's theorem and is worth global attention. Again, not too tough. All this time I have just been looking for a mathematician to help write up the proof and I would share credit if due. I am in busy season and do not have time for these games. CRGreathouse, you were rude to me, but do not worry. I am not loosing sleep at this point over this theorem. Best of luck guys.
February 13th, 2012, 12:41 PM   #27
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Re: Full Paper - Conjecture 9-14-11

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 Originally Posted by ChristopherM I'm just a sockpuppet.... Again, I am an accountant, not a Math geek. You guys are anal in my book... who cares!! Decimal-shmecimal... A valid disproof of Cantor's diagonal argument spells trouble for Godel's theorem and is worth global attention. Again, not too tough. ...
Who cares? Mathematicians care.

 February 14th, 2012, 05:54 AM #28 Newbie   Joined: Feb 2012 Posts: 15 Thanks: 0 Re: Full Paper - Conjecture 9-14-11 My apologies to the real mathematicians out there. In my opinion, they should give you your phd while you are going to school and then take it away from you when you graduate so you do not become an idiot. I have been ridiculed and told I was crazy for quite some time now, which has literally been driving me crazy, but I have been wishing to end this paper with a plea for world peace and understanding. That starts with humility. From the closing remarks, the world's greatest paragraph explained: That is what blinded himyou (a left bracket, {). That is what blinded youhim (a right bracket, }). Both statements are equal (the axiom of extensionality is not always able to be considered consistent). The statements are coming from the same person (a mathematician). One implies a person is being spoken to (a listener, student, or the accused) and one implies a person is being spoken about (the speaker, the teacher, or the accuser). The problem occurs when both people are in the room (the paradox is that we would fight about this). Let there be light
February 14th, 2012, 08:23 AM   #29
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Re: Full Paper - Conjecture 9-14-11

Quote:
 Originally Posted by ChristopherM CRGreathouse, you were rude to me, but do not worry.
I certainly didn't intend to be. Looking over what I wrote, I don't see anything rude.

Quote:
 Originally Posted by ChristopherM Doing so results in the set "RI" as defined in the paper. Each element of RI is an infinitely large set of finite binary strings that approach the infinitely large string used to define the element. From here, it should be obvious that the union of all elements in the set RI will equal the set of all finite binary strings. Omit one element of RI from the union, however, and you no longer have the set of all finite binary strings. Omitting one element of RI from the union would leave at least one (or infinitely many) missing finite strings from the resulting union. Therefore, given that the finite binary strings are enumerable (flipping each binary integer accross a decimal point will result in the set of all finite binary strings), so must be the infinitely large ones. That is why the theorem, "... for any element 'j' in RI, 'j' is not a subset of the union of all 'g' in RI such that 'g' is not equal to 'j'" is a disproof of Cantor's theorem if accepted. Not too tough.
Your proposed proof is incorrect. In short, since you're in busy season: $\{0,1\}^\omega\ne\bigcup_{n=0}^\infty\{0,1\}^n.$ IOW, the key sentence above starting "Therefore" is incorrect.

It's OK; it's common for people to be confused by Cantor's proof. Even I, when I was first introduced to it, thought it might be wrong (I had an incorrect extension of the proof of the countability of the rationals to the reals). But I brought up my thought to the professor who explained where I had made a mistake and I learned from it. Perhaps you will do the same eventually.

 February 14th, 2012, 10:32 AM #30 Newbie   Joined: Feb 2012 Posts: 15 Thanks: 0 Re: Full Paper - Conjecture 9-14-11 I appreciate your time CR. I first learned about Cantor's Theorem over 7 or 8 years ago and am not confused. The equations you give are not applicable. We are dealing with the set RI, which has the same cardinality as the set of all reals on the range (0, 1], but is by no means equal to the set of all reals on the range (0, 1]. Union all elements of RI together, except one, and you have a set with cardinality that is strictly less than the cardinality of the set of finite binary strings. Union the last element of RI, which I like to say is { .1, .11, .111, .1111, ...}, and you finally get the set of all finite binary strings (or dyadic reals... whatever you call them). The sentence starting with "therefore" is therefore correct as far as I can tell. Thanks again.

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