New Anti-Cantor Attack
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From: George Greene on 1 Jun 2010 15:09 On May 30, 2:00 am, Transfer Principle <lwal...(a)lausd.net> wrote: > But what about Herc's proof attempt? Some of us have been here for over 25 years. Maybe you should ask instead of telling. > Let's see: > > > N= { > > 1, > > 2, > > 3, > > 4, > > ... > > } > > Let's calculate a new natural MAX+1. > So Herc lists the elements of N. But then one wonders, > what is the fifth element of Herc's list, given that its > first four elements are 1,2,3, and 4? That is not even the point. THE POINT is that "MAX" IS AN UNDEFINED TERM in this context: Herc's "enumeration" DOES NOT HAVE any value "MAX". He hasn't even said what he wants or expects MAX to mean! > > That is 4+1 = 5 > > in this finite subset example. > > Voila 5 is a new number not in N OK, so NOW we know that Herc thought that MAX=4. But in that case, he should've written > > N= { > > 1, > > 2, > > 3, > > ... > > 4 (=MAX) > > } AS OPPOSED to what he actually wrote. It's best to cite the first error first, usually. > > Therefore no matter how big N is there is always a new element > > that can be listed and therefore the size of the > > set N is bigger than infinity. > > If Cooper is assuming that N is the set {1,2,3,4}, then he > has just proved that card(N) is greater than _four_, not > countable infinity (aleph_0). No, he's done better than that; he's proved that for ANY (natural) value of MAX, card(N) > MAX. He really has proved the existence of a new kind of cardinal (for the cardinality of this set), given that he's proved that no natural is its cardinality. Sure, I know he said 4, but BEFORE that, he said MAX, and he didn't put any particular value on it. So in some sense he would've had the correct proof, if he just hadn't put the ... ' s at the end of his "enumeration" WHILE trying to claim that it STILL had a MAX value. In any case, seriously, it is bad (seriously, bad) for you to try to talk TO US about this. Please address your objections to Herc himself, and please try to focus on one or two specific ones per message. Otherwise you're just masturbating in public.
From: Jim Burns on 1 Jun 2010 15:30 Bart Goddard wrote: > Jim Burns <burns.87(a)osu.edu> wrote in > news:hu3hll$jqd$1(a)charm.magnus.acs.ohio-state.edu: > >> The point (my point, Herc's point) is that >> the worth of the argument is not determined by >> the worth of the arguer. > > How do you propose that a worthless arguer > come up with a good argument? Maybe "determined" > is too strong a word, but at the very least, > the correlation coefficient here is .999.... It sounds like "explain" instead of "propose" may be what you meant above. Since I don't know how to answer your question with "propose", I will answer it with "explain". I don't have to explain how a worthless arguer could come up with a good argument. I just have to evaluate the argument, good or poor. Suppose that the correlation coefficient is ..999... . Is that a good counter-argument? If it is, then I have a gift for you: the probability that Goldbach's Conjecture is true is > 0.999. Go and publish! You'll be famous! (You're welcome.) Perhaps I misunderstand you, though. If you are using the correlation coefficient between an arguer and their arguments to pick which arguments to invest your time in, then I agree with you -- it is important to consider all the arguments of the past that turned out to waste your time. However, once you have decided to argue for or against some position, you would not use those past arguments as an "explanation" why someone is wrong, would you? The distinction I am drawing is between the beginnings of arguments and the ends of arguments. I call choosing to enter an argument the beginning of an argument, and I think that there should be no broad standards for choosing to enter or not to enter any particular argument. Let it be a matter of taste or intuition: it is still your own time that you are spending. The correlation coefficient is as good as any way to choose, and better than most, but still up to the individual. I call drawing the conclusion the end of an argument. I do not know you, Bart Goddard, but I suspect that you would be insulted if I claimed that you claimed that Herc's mathematical arguments were nonsense /because/ Herc is crazy, not because of some mathemmatical fault. It is the second, non-mathematical way of judging that I think Transfer Principle is using, judging from his writing upthread "even though Herc/Cooper turned out to be not worth defending in the end". Perhaps I am mistaken. I decided to beat once again this argument- turned-dead-horse because, after some reflection, I have decided that this one point embodies most of my personal philosophy of mathematics and because it was a pleasant change of pace to agree with Herc, with whom I have dealt in the past. Jim Burns
From: Aatu Koskensilta on 1 Jun 2010 15:34 Jim Burns <burns.87(a)osu.edu> writes: > Suppose that the correlation coefficient is .999... . Is that a good > counter-argument? If it is, then I have a gift for you: the > probability that Goldbach's Conjecture is true is > 0.999. Go and > publish! You'll be famous! (You're welcome.) What sort of probability is involved here? > I decided to beat once again this argument- turned-dead-horse because, > after some reflection, I have decided that this one point embodies > most of my personal philosophy of mathematics I'm baffled. What is it in your point that is specifically mathematical? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 1 Jun 2010 15:39 Transfer Principle <lwalke3(a)lausd.net> writes: > And even though Herc/Cooper turned out to be not worth defending in > the end, that still doesn't mean that I'm going to start defending > Spight. Out of idle curiosity, how would you go about "defending" Marshall? -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: |-|ercules on 1 Jun 2010 16:12
"George Greene" <greeneg(a)email.unc.edu> wrote ... > On May 29, 11:36 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > >> Yes I know it's such a simple yet equivalent logical deduction of 'bigger than infinity' >> and really shows how dumb Cantor subscribers are to miss that, > > No, it isn't. > Your second proof is a deduction of "bigger than FINITE" because > all the lists you are generalizing over ARE FINITE -- they have a last > MAX element. Even though you were too stupid to draw it that way. > If the list actually is a list of all the naturals in order then IT > HAS NO MAX, > and your proof can't even get started. > >> but the fundamental mathematical truths are generally quite simple. > > Of course they are, yet despite this, you are too stupid to apply > them. This is not worth arguing because no one in sci math will recognize ANY valid new result, but this is my last post on the topic. You all SAY that the 'new subset' works in the infinite case and MAX only works on any finite case. But you also show HOW you get a 'new subset' with finite examples. It works so well with finite examples!!! That is why you are all fooled. 1 - {1,2} 2 - {3,4} 3 - {5,6} the box containing the numbers of all the boxes that don't contain their own number is.... there is none... the numbers of all the boxes that don't contain their own number is.. {2,3} IT'S NOT IN THE LIST It seems to work, as demonstrated in the finite case, so you are all fooled that the logical deduction for the infinite case is legitimate. Your entire proof/belief/philosophy of higher sets than infinite size, relies on the fact that there_is_no_box_containing_the_numbers_of_all_the_boxes_that_don't_contain_their_own_number! That's your religion! You can compute every possible digit sequence up to infinite length, you can compute every possible subset of N up to infinite length, but that doesn't bother any of you, because it's in your text book. Herc |