THE HOLY GRAIL ~ CANTOR DISPROOF
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From: master1729 on 29 May 2010 12:54 lwalke wrote : > On May 27, 7:32 am, William Hughes > <wpihug...(a)hotmail.com> wrote: > > On May 27, 1:10 am, Transfer Principle > <lwal...(a)lausd.net> wrote: > > > Probability? Random? > > It is true that the set of counterexamples may have > measure > > 0 in the usual Lebesgue measure. Indeed, I suspect > > this, though I cannot see a simple way of > demonstrating it. > > However, the set of counterexamples is non-empty > and uncountable. > > Thanks. > > > [Note that the idea that an infinite number of > reals can have > > Lebesgue measure 1 already requires uncountability. > If you insist on > > trying to make Herc's statements consistent you > will need a > > theory of probability in which a countable infinity > of elements, > > each with the same probability, has a probability > of 1.] > > Yes, I've heard of the proof that any countable set > must have > measure zero (since we can cover the first real on > the list by an > interval less than epsilon/2, the second real by an > interval less > than epsilon/4, the third less than epsilon/8, and so > on). > > This idea has also come up in the tommy1729 threads. > In > particular, tommy1729 was trying to discredit the > Axiom of > Choice, which is used in the proof of the existence > of a > non-Lebesgue-measurable set. The usual proof entails > using > AC to come up with a set such that the countable > disjoint > union of images of the set under rigid motions is the > entire > unit interval. Now tommy1729 pointed out that the > only way > for this to work would be to assign a nonzero > infinitesimal as > its measure. Since standard analysis does not permit > nonzero > infinitesimals, this is not done, and instead the set > is declared > to be nonmeasurable. not only to discredit the axiom of choice , but the entire concept of " nonmeasurable " set. (in fact choice and non-measurable together doesnt even seem right ...) however i dont think *that particular* idea violates ZF. maybe ZF~non-measurable is constructable ?? then again if *that particular* idea doesnt violate ZF , ZF = ZF~non-measurable might be true... or at least consistant. ZF~C implies no non-measurable sets , as i seem to recall proven ... by ... some guy in 19 ... > > Of course, it would be pointless to attempt to come > up with > such a theory for Herc since it's unlikely that Herc, > who > appears to doubt the existence of uncomputable reals, > would > suddenly accept nonzero infinitesimals instead. And > even if > he did, Herc isn't cuurently active in this thread. > > It might be worth coming up with a theory of > noninfinitesimal > measure for tommy1729. But we must remember that > tommy1729 rejects ZFC and instead proposes an > alternate > theory, which he calls TST. Although it might be an > interesting > exercise for me to attempt to axiomatize TST, we must > recall > that TST is completely different from ZFC as it's > based on > mereology and three-valued logic. So we would be > required to > come up with the three-valued logic (including new > rules of > inference), then the mereology, then sets. Only then > could we > come up with reals, sets of reals, and their > measures. But > I'm likely to be stuck at the three-valued logic, > trying to come > up with laws of inference that both tommy1729 and the > others > are willing to accept. Most posters would have > abandoned > the thread by the time I even reached mereology, much > less > measures of sets of reals. > > At this point, I do wish to consider a single poster > to defend, > and work on a theory for just that one poster. But > I'm still > stuck on which poster to choose. I was earlier > considering > AP, but I fear that it will be difficult to separate > AP-reals from > Atom Totality, just as the posters in this thread had > trouble > separating computable reals from Genesis Adam. > > So AP is out. As I already mentioned, tommy1729 is > out. im out. oh well. regards tommy1729 // working on tetration //
From: master1729 on 29 May 2010 13:34 lwalke3 wrote : > On May 27, 3:31 pm, "|-|ercules" > <radgray...(a)yahoo.com> wrote: > > "Transfer Principle" <lwal...(a)lausd.net> wrote .. > > > I definitely do _not_ accept Herc/Cooper's claim > that > > > he is Genesis Adam, since, to say the least, Adam > is > > > _dead_ according to Genesis (for having eaten the > > > forbidden fruit). How can someone be a specific > > > person mentioned in a book if according to that > book, > > > that person is dead? (Unless that book is wrong, > of > > > course but Herc/Cooper also states belief that > the > > > book is true.) > > Well that's it for me and sci math you have your > wish. When people stop blatantly lying in my face > I'll check again in 100 years. > > And this is exactly what I was trying to avoid. > > In another thread, there was a long discussion about > how I > should stop being so quick to defend the so-called > "cranks" > and start allowing for the possibility that what they > are > saying might be "wrong." Jim Burns, Jesse Hughes, and > others convinced me that I am more likely to be > respected > (and less likely to be killfiled) by posters, if only > I would > consider the possibility that the "cranks" are > "wrong." > > So what happens? I decide to consider the possibility > that > Herc might be wrong. And then Herc becomes offended > and decides to stop posting. > > One word that I told myself that I'd try to use less > often is > "bully" -- in particular, I wanted to stop referring > to other > posters as "bullies." But right now, I need to call > _myself_ > (and only _myself_) a "bully." For that's exactly > what I > just did. I just "bullied" Herc out of sci.math. > > What did I do to offend Herc? First, when he made a > mathematical claim, I told him that ZFC refutes his > claim > and gave him a proof of this. I avoided assuming that > ZFC > is the only possible theory or only theory worth > considering, > but merely told him that ZFC refutes his claim. > > Herc's response? > > > Translation, "No because I told you so". > > Next, I tried to show Herc a specific counterexample > to his > claim, still working in ZFC. > > Herc's response? > > > You are selecting specific diagonals based on the > list. > > reminding me that his claim was probabilistic in > nature. > > But the straw that broke the camel's back wasn't even > mathematical in nature. It was a discussion about > Genesis > Adam, which I was trying to avoid. But I had to say > in > passing to Aatu (who had just criticized me for > trying to > defend Herc) that I don't consider Herc to be Genesis > Adam, > and do reiterate that I consider all discussion about > Adam to > be off-topic for sci.math in the first place. > > Herc's response? > > > ps that's the dumbest [expletive] rebuttal of > Genesis possible > > And then he leaves, because I have just "bullied" him > away. thats why you shouldnt defend Herc or Burt and the 'alike'. 'alike' needs to be defined ; these people are the indefensibles , either for being completely wrong , completely incompetant or completely unstable. you should avoid : religion , 0.99999 , collatz and hypersensitive people. math requires attitute. especially with a controversial or unpopular idea , claim or result. some tried to bully me away too. but one needs to be strong. not pretend. i dont blame certain people for leaving and getting bullied away. sometimes its for the best ; no good idea ; not admitting being wrong ( in ALL possible interpretations and axioms ) math requires attitude. but not attitude to replace those who dont have attitude or anything meaningfull to say. you shouldnt feel guilty about it. some people are emo. if they feel insulted by you , they usually are oversensitive and not suitable for an unmoderated forum. going off-topic to religion and/or posting meaninglessness or 'yet another same' thread ( another 0.999 ) only makes it more justified not to get involved. only an emo could see you as a bully. if he is wrong by ZFC he is wrong by ZFC. > > It's threads like these that make me want to go back > to my > habit of defending "cranks" at all costs. I'd much > rather be > overly accommodating to Herc than be the poster who > is > responsible for scaring Herc away. If galathaea were > still > here, I bet she'd be pointing her finger directly at > me for > being the "bully" who "scared" Herc away. far from galathaea. your projecting yourself onto galathaea. in fact galathaea is more different than you think. you seem to have forgotten that galathaea and myself had flamewars. we didnt get along in the beginning. she considered me arrogant and other things. but she learned out that for instance i knew about her multisections , whereas other didnt. my skills and attitude and the fact that i stayed and didnt let myself get bullied away , made her appreciate me. she assumed that regular posters knew about her multisections , since series multisections was actually a ' defined term in standard math '. she even recieved bad comments surrounding multisections and mereology. but here i ideas were closer to mine than she realized ever before. she identified herself with the standards , because she knows the standard math. but that was wrong. her math - not her personality - is closer to 'tommy1729'. since i was the only guy of that kind she started to defend and appreciate me. even a cult. she was also a friend of quasi and as me , was against the ' abolish fraction apologetics ' especially if those apologetics were rude to us ( gala , quasi and tommy1729 ) calling them hypocrites. she wouldnt point a finger at lwalke. she left sci.math out of despair , but i know she still misses me. > > And it was all because Aatu criticized me for > defending Herc, > and I had to react to his criticism. > > What I want to be able to do is speak to posters like > Herc in > such a way as not to be a "bully" to them, yet avoid > drawing > criticism from others, like Aatu in this thread. And > so the > next time someone posts a claim refuted by ZFC, I > defend > their claim, and someone criticizes me for doing so, > then I'll > be sure to remember this thread, the thread in which > I > bullied and scared Herc away. cantors diagonal argument is not wrong. it doesnt even require ZF , it just isnt wrong. it can only be misunderstood. which isnt your fault. the REALS ARE uncountable. you certainly shouldnt be overly accommodating ! you didnt even get a chance to explain or apologize ( which you shouldnt in the case of herc ). similarly herc shouldnt feel bad for leaving. it was the best thing ... as God intended ... :p regards tommy1729
From: Transfer Principle on 1 Jun 2010 15:15 On May 29, 7:23 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On May 28, 8:45 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > Then what should I do the next time someone makes a claim > > that is refuted by ZFC? I suppose that I should continue to > > do what I did in this thread, and consider all the main reasons > > that someone might make such a claim. > No, silly boy. You should say what you think the truth is, > and why. In another thread, a poster made a claim about Cantor that is refuted by ZFC. And so I listed the four possible cases, as usual, only to have another poster, Waldby, say that even listing the cases is still considered "patronizing." And we can see what the problem here is: To tell a poster that he is right when he is right is OK. To tell a poster that he is right when he is wrong is patronizing. To tell a poster that he is wrong when he is right is bullying. To tell a poster that he is wrong when he is wrong is OK. We know that posters don't want to be bullied, and we know that they don't want to be patronized. But what I fear is that even to list the _possibility_ that a poster is right when he is wrong is patronizing (and vice versa for bullying). That is to say, if a poster contradicts ZFC, that poster might either be right about an alternate theory or wrong about ZFC. To tell a poster that he is right about an alternate theory when he intends to talk about ZFC is evidently patronizing (and I'll accept that), but even just to _ask_ (not _tell_, but _ask_) him whether he's using an alternate theory (when he isn't) is _still_ patronizing? I still want to be able to ask questions, even if the answer of the questions happens to be "no," without being patronizing (or bullying, since some questions may sound like bullying). But instead, this would mean that I can't respond to a post attacking Cantor without _knowing_ (not _asking_, but _knowing_) whether the OP is right or wrong. > Look, if you'd just [...] listen to your elders [...] That's what I've been trying to do! And so let me combine the suggestions of Greene, Spight, and Waldby and come up with a new plan of how to respond to a post attacking Cantor. Instead of listing the four cases -- Waldby mentioned a Case 5, but even if I added this fifth case, someone in the future might mention a Case 6, and then we can never be sure that the list is exclusive or exhaustive -- I can address the main cases without enumerating them. Example: Hypothetical OP: "Cantor is wrong because ..." (followed by an argument that is flawed wrt ZFC). My response: I have nothing against theories other than ZFC. But ZFC, the standard theory, proves that there exist uncountably many real numbers. Here's why the OP's argument fails in ZFC: (followed by an explanation of how the argument is flawed wrt ZFC). If the OP is referring to a theory other than ZFC, then I'd like to know more about this theory. How do the axioms of the new theory differ from those of ZFC? Which axioms of ZFC does the OP reject? Is the OP considering NFU? (End of response) And so this covers the three suggestions. Waldby suggests that I respond with a mathematical post. I would argue that a post which entirely discusses a theory other than ZFC is still mathematical, but the problem is that I wouldn't know enough about which theory the OP has in mind in order to make a coherent post. Thus, until I know more about the theory, the mathematical content in the post would have to come from ZFC or standard theory. Therefore, my post can describe why the OP's argument is flawed in ZFC. Greene suggests that if a poster rejects ZFC, I find out which specific axioms the poster is rejecting. And Spight suggests that I post what I think the truth is, though I can't be sure what the truth is until I know whether the OP is discussing ZFC or not. And so I can acknowledge this. As it turns out, I have the opportunity to demonstrate these better posting habits right away. In another thread, a poster has claimed that N and C are isomorphic. I've already posted in that thread in order to clarify that the poster really does mean to say that N is isomorphic to _C_, and not to merely a _subset_ of C. So I can now follow the suggestions from this thread and point out why ZFC proves that N is not isomorphic to C, as well as ask about alternate theories in which N is isomorphic to C.
From: Transfer Principle on 1 Jun 2010 15:24 On May 29, 12:46 am, "|-|ercules" <radgray...(a)yahoo.com> wrote: > "George Greene" <gree...(a)email.unc.edu> wrote > > The most irritating of the cranks will > > refuse to specify their axioms, or attack the legitimacy of "the" > > axiomatic "method". > Why is the axiomatic method legitimate? > Bonus points if you can demonstrate this from axioms! Here Cooper questions the legitimacy of the axiomatic method. He is hardly the first sci.math poster to do so. Regarding the four cases that I've listed earlier, I'd consider rejecting the axiomatic method to be part of Case 2. Such posters realize that one can use (the ZFC) axioms to prove an undesirable result, and since the result is undesirable, rather than reject the theory, they reject the axiomatic method altogether. The poster WM is notorious for rejecting the axiomatic method, and now Herc is also leaning in that direction. I wish that posters who find the results proved from a theory to be undesirable would reject just that _theory_, and consider other theories which prove more desirable results. NFU proves the existence of non-Cantorian sets for posters who reject Cantor, while Pocket Set Theory, ZF-Infinity, and others abound for those who don't like sets that are as large as some of those whose existence is proved in ZFC.
From: Aatu Koskensilta on 1 Jun 2010 15:25
Transfer Principle <lwalke3(a)lausd.net> writes: > We know that posters don't want to be bullied, and we know that > they don't want to be patronized. I want to be bullied and patronized. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus |