Give me ONE digit position of any real that isn't computable up to that digit position!
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From: |-|ercules on 7 Jun 2010 22:00 "David Bernier" <david250(a)videotron.ca> wrote >> >> NO BOX EVER CONTAINING THE NUMBERS OF BOXES NOT CONTAINING THEIR OWN NUMBER >> MEANS HIGHER INFINITIES EXIST. >> >> TRUE OR FALSE? >> >> >> BTW, dozens of famous mathematicians dispute Cantor's proof, so maybe >> having a 95iq >> is a basis for not following it, but not "following" it is not a basis >> for a 95iq. > > How should one go about defining existence? As in higher infinities exist? That's very deep and profound, the type of answer that might pop into my head in a few days time. Would you rather say "higher infinities" are useful descriptions for certain operations? Technically matter doesn't exist, what would it be made of? an indivisible solid with infinitely fine coarseness? but there are simple postulates, Ex - something exists, our perception of reality exists, patterns exist, time exists. Winograd (winning graduate?) programmed a talking computer that defined/parsed each word as a program. It knew nothing except how to pick up blocks and put them down again, but in it's own world it was just brilliant! Herc
From: Tony Orlow on 7 Jun 2010 22:03 On Jun 6, 1:54 am, Transfer Principle <lwal...(a)lausd.net> wrote: > On Jun 5, 10:13 pm, "|-|ercules" <radgray...(a)yahoo.com> wrote: > > > "TransferPrinciple" <lwal...(a)lausd.net> wrote .. > > > According to Knox, Herc is trying to prove that > > > classical mathematics is "wrong." And like Knox, I > > > wish that Cooper would just consider an alternate > > > theory (she mentioned intuitionism) if he doesn't > > > like classical mathematics that much. > > It's hard to prove classical mathematics is wrong when every time > > I dispute your claims you jump back to shore and say "nahh nahh > > we didn't claim anything factual we just have some axioms and derivations" > > What does Herc mean by "factual" here? Does he mean > that classical mathematics doesn't prove anything > about the real world. > > If so, then I agree with Herc to some extent. It is > true that "ZFC proves that N and R do not have the > same cardinality" is indisputable, since it does > follow from the axioms of ZFC. > > Yet one will be hard-pressed to find an uncountable > object in the real world. Indeed, some physicists > wonder whether length, time, etc., can be quantized > (Planck units), which would imply that there's no > real-world example of an _infinite_ object, much less > an uncountable object. > > 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 since the real world can't > prove anything about infinity, I'm open to many > different theories about infinity, including NFU, > PST (Pocket Set Theory), intuitionism, as well as > finitist set theories like ZF-Infinity in which one > can't necessarily prove that infinite sets exist. I > am even somewhat open to _ultrafinitist_ theories > where there's an upper bound on the largest natural > number that exists, as long as that upper bound is > larger than any number that can describe objects in > the real, physical world. > > > Higher infinities and incompleteness and most of your uncomputable claims are just > > platonic drivel. > > I agree (except for the word "drivel"). Would you like an example, if only in idealization, about a real-world every-day occurrence? Got one, with cosmic consequences... <3 Tony
From: Tony Orlow on 7 Jun 2010 22:06 On Jun 6, 9:13 am, Marshall <marshall.spi...(a)gmail.com> wrote: > On Jun 5, 10:54 pm,TransferPrinciple<lwal...(a)lausd.net> wrote: > > > > > Yet one will be hard-pressed to find an uncountable > > object in the real world. > > You'll never find a three in the real world either, but that > doesn't mean that three is therefore a somehow problematic > concept. > > > Indeed, some physicists > > wonder whether length, time, etc., can be quantized > > (Planck units), which would imply that there's no > > real-world example of an _infinite_ object, much less > > an uncountable object. > > Sure; so what? The point of math isn't to exactly faithfully > model the universe. There is exactly and precisely only > one *complete* model of the universe; that is the universe > itself. Any other model is necessarily leaving something > out. (Probably quite a lot in fact.) > > > > Higher infinities and incompleteness and most of your uncomputable claims are just > > > platonic drivel. > > > I agree (except for the word "drivel"). > > And yet there is no bijection between the natural numbers and > the real numbers. You might be able to make up a theory > in which you can prove that there is, but you won't be able > to demonstrate it, because it doesn't exist. (And from there > a trivial application of the pigeonholeprincipleshows the > existence of uncomputable reals.) > > Marshall This sounds a bit like a well-ordering of the reals. But, I have better challenge... <3 Tony
From: Virgil on 7 Jun 2010 22:40 In article <1066f7e9-d341-4179-a624-90073069e66c(a)d8g2000yqf.googlegroups.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Well, Herc, you remind me of the dark question. There's the Continuum > Hypothesis, and other questions, but in the context of the diagonal > argument (N=S^L), there remains an unanswerable question. What is the > width of a countably infinitely long complete list of digital numbers? If that list of numbers is to be complete in the sense of including all reals, then it cannot be only "a countably infinitely long complete list". > If the maximum length is finite, the list also is finite in length. If those numbers are to represent the naturals, then to be complete, the list of them cannot have any finite maximum length. > If > the list is countably infinite in width, it is taken to be uncountable > in length, according to standard theory. "Lists" are,in any kind of standard theory, pressumed to be at most countable in length unless specifically allowed to be otherwise. > What is the width of a > countably infinite list of saturated digital numbers? What in Niefflehiem is a "saturated digital number"? Are they part of the content of TO's "all wet theory"?
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 |