Give me ONE digit position of any real that isn't computable up to that digit position!
in [Math]
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From: herbzet on 8 Jun 2010 01:26 herbzet wrote: > |-|ercules wrote: > > "herbzet" wrote ... > > > |-|ercules wrote: > > >> "herbzet" wrote ... > > >> > |-|ercules wrote: > > >> >> "herbzet" wrote ... > > >> >> > |-|ercules wrote: > > >> >> >> "herbzet" wrote ... > > >> >> >> > |-|ercules wrote: > > >> >> > > > >> >> >> >> I want to hear mathematicians explain why the nonexistence of a box that contains > > >> >> >> >> the numbers of the boxes that don't contain their own number means that higher > > >> >> >> >> infinity exists. > > >> >> >> > > > >> >> >> > Who said that? Cite, please. > > >> >> >> > > >> >> >> you did. > > >> >> >> > > >> >> >> -------------------------------------------------------------------------------- > > >> >> >> > > >> >> >> > Because the most widely used proof of uncountable infinity is the > > >> >> >> > contradiction of a bijection from N to P(N), which is analagous to > > >> >> >> > the missing box question. > > >> >> >> > > >> >> >> Perhaps so, but why do you ask? > > >> >> >> > > >> >> >> -- > > >> >> >> hz > > >> >> >> > > >> >> >> ------------------------------------------------------------------------------ > > >> >> > > > >> >> > Then again, perhaps not. > > >> >> > > >> >> you can crawl back under your rock until the box question goes away. > > >> > > > >> > What question was that now? You keep moving the goalposts on us. > > >> > > > >> > Perhaps if you can manage to phrase the question with some rigor, > > >> > it is possible that you would receive a concise reply. > > >> > > > >> > > >> ok, we have boxes, all numbered from 1, 2, 3... and so on indefinitely. > > >> > > >> inside the boxes are some physical representations of natural numbers, > > >> any finite or infinite amount of them, composed of 1 of each of 1, 2, 3... > > >> > > >> can any of the boxes contain only the numbers of all the boxes that don't contain > > >> their own numbers? > > No. > > > >> what can you deduce from this? > > Among the infinite(!) number of statements I could *validly* deduce > from this statement, I could deduce that > > (1) If there is an infinite set S, then there is a set S' of > greater cardinality. What, no reply? All that drama, and no reply??? What happened to Hercules, the giant Cantor killer? Pfft. -- hz
From: Transfer Principle on 8 Jun 2010 12:19 On Jun 6, 2:57 pm, Ostap Bender <ostap_bender_1...(a)hotmail.com> wrote: > On Jun 5, 8:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > There have always been posts criticizing Cantor and ZFC > > here on sci.math, but for some reason, ever since we > > turned the calendar to June, the number of such posts and > > threads has exploded! > It's the tick season! > >So let me try to keep up with all > > of these threads. > Make sure to do that. Review and respond to each and every post by > anti-Cantor kooks. And yet Bender sees fit to review and respond these anti-Cantor "kooks." Therefore, it's OK for me to respond to all the anti-Cantor "ticks" if and only if it's OK for Bender to do so. Also, the mathematician Willard van Orman Quine came up with a perfectly respectable theory which proves the negation of Cantor's Theorem. Thus, according to Bender's logic, Quine must have been an anti-Cantor "kook" as well.
From: William Hughes on 8 Jun 2010 12:38 On Jun 8, 5:40 am, Graham Cooper <grahamcoop...(a)gmail.com> wrote: > > 2/ all possible digit sequences are computable to all, as in an > infinite amount of, finite lengths > > This contradicts that a *new sequence* can be calculated by modifying > the diagonal, Nope, every one of the finite length sequences has a last element. The new sequence does not have a last element. - William Hughes
From: Transfer Principle on 8 Jun 2010 13:20 On Jun 6, 10:10 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > On Jun 5, 10:54 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > the real world. Back in March, I had the following discussion with MoeBlee: Me: > > [If] JSH were to state that the sky is blue, the _standard theorists_ > > would be the ones to start coming up with obscure counterexamples > > such as the Doppler effect at velocities approaching c, alien > > languages in which "blue" means "red," and so forth. MoeBlee (9th of March, 8:37AM MoeBlee's local time): "The standard theorists" would do that? How do you know? WHICH "standard theorists"? And would you please say exactly what you mean by "a standard theorist"? MoeBlee was skeptical that an adherent of standard theory would come up with obscure counterexamples to generally accepted facts. I wanted to find an example of this, but at the time I couldn't find one. So I told MoeBlee that I would wait until someone actually made such a post, then jump on it as soon as I see it. And right now, I see such a post. Let's see what Fred Jeffries has just written: > > It is precisely for this reason that I am open to > > reading about alternate theories, as long as those > > theories don't contradict empirical evidence. Thus, > > even I won't defend a theory which seeks to prove > > that 2+2 = 5, since one can prove in the real world > > that 2+2 = 4, not 5. > But there's a great yet-to-be-discovered cryptographic system based on > a system where 2 + 2 = 5. Not to mention rabbit breeding or bowling (I > get 6 pins with my first ball, 4 with my second, 8 with my third and > roll a gutter ball with my fourth. What's my score?). (I forget how bowling is scored, but IIRC, 6+4 is a spare, which means that the next ball counts for a double score. This 6+4+8 = 26.) And so Jeffries has just done what MoeBlee, back in March, asserted that posters like Jeffries would not do at all. He contradicts the accepted facts of standard arithmetic by coming up with an obscure counterexample from bowling (obscure in that it would hardly come up in a mathematical discussion). The point that I want to make is that Jeffries is being granted a freedom that Herc isn't. Jeffries is allowed to consider theories which he believes can model a variety of real-world situations, including 7D geometry, bowling arithmetic, and other ideas mentioned in his post. If Jeffries is allowed to choose alternate theories based on how well they model situations, then Herc should be allowed to as well. If Herc believes that "Cantor is false" models the real world, then he should be allowed to hold that belief. But that's not how things work here at sci.math. When Cooper contradicts ZFC, he is then criticized for not conforming to ZFC. When Jeffries contradicts ZFC, he isn't so villified. When Herc says, "Cantor is wrong," he is called an anti-Cantor "kook." When Jeffries says, "6+4+8 = 26 in bowling," he isn't called an anti-Peano "kook." And yet I'm the only person who can see this blatant double standard? I have nothing against theories other than the standard which can model real situations, such as Bowling Arithmetic. I am opposed to those who use such theories but require others to use only the standard theory. But as far as active posting is concerned, I've decided to draw the line between PA and ZF. So, if a poster were to say, "PA is wrong because in bowling, 6+4+8 = 26," then I wouldn't post in that thread at all. But if a poster were to say, "ZF is wrong because the universe is finite," then I will defend that poster. So I defend posters who attack ZF, but I don't defend (but nor will I actively oppose) those who attack PA. So Jeffries is free to use 7D geometry, Bowling Arithmetic, Hyper-Mahlo cardinals, and whatever else he feels describes the real world. All I ask is that Herc be granted that same freedom.
From: MoeBlee on 8 Jun 2010 14:08
On Jun 8, 12:20 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > On Jun 6, 10:10 am, FredJeffries <fredjeffr...(a)gmail.com> wrote: > > > On Jun 5, 10:54 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > > the real world. > > Back in March, I had the following discussion with MoeBlee: > > Me: > > > > [If] JSH were to state that the sky is blue, the _standard theorists_ > > > would be the ones to start coming up with obscure counterexamples > > > such as the Doppler effect at velocities approaching c, alien > > > languages in which "blue" means "red," and so forth. > > MoeBlee (9th of March, 8:37AM MoeBlee's local time): > "The standard theorists" would do that? How do you know? WHICH > "standard theorists"? And would you please say exactly what you mean > by "a standard theorist"? > > MoeBlee was skeptical that an adherent of standard theory > would come up with obscure counterexamples to generally > accepted facts. I don't know what particular comment of mine you have in mind. Please include what I was responding to when I said "would do that"? What EXACTLY is the "that" that I was speaking of? Meanwhile, I don't even know what YOU mean by "adherent of standard theory". You even just QUOTED me as asking WHAT do you mean by "standard theorist"? As far as I can tell, you still seem to think as if there are two political parties, the "Standards" and the "Rebels" so that people in these threads neatly and naturally fall into one or the other camp. I have a cluster of notions and interests and questions regarding all kinds of theories and various methods of logic even. I've never taken any pledge of allegiance to ZFC or even to first order logic or whatever. You've never quoted anything by me that determines I'm a "standard theorist" and still without your saying what the hell constitutes a "standard theorist". > I wanted to find an example of this, but > at the time I couldn't find one. So I told MoeBlee that I > would wait until someone actually made such a post, then > jump on it as soon as I see it. > > And right now, I see such a post. Let's see what Fred > Jeffries has just written: > > > > It is precisely for this reason that I am open to > > > reading about alternate theories, as long as those > > > theories don't contradict empirical evidence. Thus, > > > even I won't defend a theory which seeks to prove > > > that 2+2 = 5, since one can prove in the real world > > > that 2+2 = 4, not 5. Again, please include the context of my comment that has anything to do with "obscure counterexamples to accepted facts". What does that even MEAN? If something is a fact, in what sense does it have a counterexample? And what kind of facts? Empirical facts? Finitistic mathematical facts? > > But there's a great yet-to-be-discovered cryptographic system based on > > a system where 2 + 2 = 5. Not to mention rabbit breeding or bowling (I > > get 6 pins with my first ball, 4 with my second, 8 with my third and > > roll a gutter ball with my fourth. What's my score?). > > (I forget how bowling is scored, but IIRC, 6+4 is a > spare, which means that the next ball counts for a > double score. This 6+4+8 = 26.) > > And so Jeffries has just done what MoeBlee, back in > March, asserted that posters like Jeffries would > not do at all. Again, what EXACTLY did I assert? I surely never asserted that I could predict what any given poster would or would not do. This is ridiculous, Transfer Principle. Please QUOTE exactly what I said that you think constitues an assertion by me that there would never be a poster who would do such and such a thing. OF COURSE there may be all kinds of posters who have all kinds of beliefs they might post! > He contradicts the accepted facts of > standard arithmetic by coming up with an obscure > counterexample from bowling (obscure in that it > would hardly come up in a mathematical discussion). He does? I really don't see how a system of scoring in bowling contradicts any finitistic mathematical fact. One can devise all kinds of scoring methods for all kinds of games (even formal games). That doesn't contradict finitistic mathematical facts. > The point that I want to make is that Jeffries is > being granted a freedom that Herc isn't. Jeffries is > allowed to consider theories which he believes can > model a variety of real-world situations, including > 7D geometry, bowling arithmetic, and other ideas > mentioned in his post. I haven't disallowed Herc from devising any theories or models he wishes to devise or consider. On the other hand, I can't get Herc to even recognize what it means for a sentence to be a theorem from a set of axioms. Herc is the one critical of a particular mathematical theory. It's fine with me that he is, but his criticisms are not even coherent. He's obsessed with asking whether a certain analogy about boxes (which he still doesn't know how to state properly, even though I've shown him how a few times - he leaves out the "and only" clause) proves uncountability. I expain to him that it's an analogy and that the ordinary proof in Z set theory relies on certain axioms and first order logic. This he does not hear. That numerals such as '1', '2', etc. and symbols such as '+' may have interpretations other than in ordinary arithmetic is not at all disputed. Of course we get different truth values for "2+2=5" in different interpretations. Anyone who has studied Math Logic 101 knows this. So what? > If Jeffries is allowed to choose alternate theories > based on how well they model situations, then Herc > should be allowed to as well. Of course he can choose any theory he wants to choose! And WHAT theory is he choosing? > If Herc believes that > "Cantor is false" models the real world, then he > should be allowed to hold that belief. Who's stopping him? Where did I even claim one way or the other on the question whether "ZFC models the real world"? Where did I even assert that there is or is not such as thing as "the real world"? First I'd have to know what you or Herc or anyone even MEANS by "the real world". There's a whole history of philosophy and all kinds of philosophical notions about reality that I take into account. If you are SINCERELY interested in some of my thoughts about this, then look up my posts where I've touched on such matters (as a mere introduction to my NON-professional and modest, tentative inclinations on such matters). > But that's not how things work here at sci.math. > > When Cooper contradicts ZFC, he is then criticized > for not conforming to ZFC. I never criticized anyone for not "conforming" to ZFC. (Of course, IF one presents something as if within ZFC that is not within ZFC then it is correct to point out that, contrary to their representation, their argument or supposed "reductio" or whatever, is not a ZFC argument or not a reductio in ZFC). I've critized people for incorrectly and ignorantly shooting their fat mouth off about ZFC. Have whatever theory you like. But Herc does not present a theory. Rather, he presents a bunch of confused and dogmatic rambling. He doesn't even know what ZFC IS. Object to ZFC as much as you like. But if one's objections are incorrectly premised or confused or ignorant as to what ZFC is, then I'll point that out if I wish. That is not denying anyone the prerogative still to hold philosophical objections to ZFC or to aspire to a different theory let alone to actually presenting a theory. MoeBlee |