An uncountable countable set
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From: Virgil on 19 Sep 2006 02:49 In article <bd51c$450e7ab1$82a1e228$28828(a)news1.tudelft.nl>, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > I don't really refuse the idea of infinite sets. (How else could I do > my calculus stuff ?) I only refuse the idea that the infinite can be > something which is essentially different from the _finite_. In short: > infinity is just finity in disguise. So infinite sets exist only when HdB finds them convenient, but not when he doesn't.
From: Han de Bruijn on 19 Sep 2006 04:04 Mike Kelly wrote: > Han de Bruijn wrote: > >> I'm just snipping the parts that don't belong to the subject "Given ... >> blah .." Nothing dishonest, just sizing down the universe of discourse. > > Huh. No, you're quoting me out of context, repeatedly. Looking at your > antics in other threads you appear to make quite a habit of this so I > don't suppose I'll be able to disuade you. Huh. Here is a copy of the common alternative. It's from: http://groups.google.nl/group/sci.math/msg/ffc930a49e1c908a?hl=en& > Tony Orlow wrote: >> Matt Gutting said: > >>>Tony Orlow wrote: > >>>>Matt Gutting said: > >>>>>Tony Orlow wrote: > >>>>>>Matt Gutting said: > >>>>>>>Tony Orlow wrote: > >>>>>>>>Matt Gutting said: > >>>>>>>>>Tony Orlow wrote: > >>>>>>>>>>Matt Gutting said: > >>>>>>>>>>>Tony Orlow wrote: > >>>>>>>>>>>>cbr...(a)cbrownsystems.com said: Hence: no. You'll not be able to disuade me. I never send a letter back when I'm answering one and don't know where this idiot habit comes from. But maybe I'm becoming too old to understand .. Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 04:17 Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote [ OK, let's keep the quotes intact this time ]: >> >>>Han.deBruijn(a)DTO.TUDelft.NL wrote: >>> >>>>Mike Kelly wrote: >>>> >>>>>You claimed that you have a very much better understanding of >>>>>probability than me. Since you know nothing of my knowledge of >>>>>probability other than that I disagree that it is meaningful to discuss >>>>>the probability of "a natural" being divisible by 3, [ ... snip ... ] >>>> >>>>What more evidence do we need, huh? >>> >>>Given that this is a *theorem* of probability theory I am mystified as >>>why this is evidence that I don't understand probability. Do you have >>>some alternative probability theory? >> >>The problem is the layer below Probability theory: Set theory. You say >>it correctly here: > > So.. are you still claiming I don't know understand probability? Did > you ever actually mean it or was it just a stupid thing you felt better > for saying? We will see how much you understand of it after the next poster. >>>>The good news is that you are doing wrong only _one_ thing: infinitary >>>>reasoning. You think that completed infinities do exist. >>> >>>If you don't accept the existence of a set of natural numbers then you >>>don't accept the set theory that probability theory is based upon and >>>you haven't suggested an alternative. Indeed, it seems somewhat odd to >>>complain about the conclusion of a theorem discussing an object you >>>don't accept even exists. >> >>The infinitary part of set theory that underpins probability theory is >>IMHO the only problem. > > Then it's stupid to attack probability theory as it obfuscates what > your real disagreement is. Wish I could untie probability theory from infinitary set theoretical foundations ... >>>>Once you stop >>>>thinking this way, everything falls in its place and you will see that >>>>it is quite meaningful to discuss the probability of "a natural" being >>>>divisible by 3. >>> >>>It is meaningful to say that a natural drawn uniformly at random from a >>>set of consecutive naturals 1 thru 3n has a 1/3 probabaility of being >>>divisible by 3. Nobody disputes this. But talking about the probability >>>of "a natural" being divisible by 3 implies a uniform distribution over >>>the naturals. Such a thing does not exist. >> >>The core of the matter is that THE naturals can only exist as a set of >>consecutive naturals 1 thru n where n is large and undefined. > > Why? Because completed infinities do not exist. >>Any such set is equipped with a uniform distribution. And hence "THE" naturals. > > Such a set doesn't contain all naturals, so in what sense is it "THE" > naturals? All naturals do not exist. What is "all"? >>This does not say that meaningful answers (i.e. independent of n) can >>always be obtained. But: mainstream mathematics HAS found a way out of >>al this. It's called the theory of "natural densities" or some such .. >>Why not substitute? But this belongs to another thread: >> >>http://groups.google.nl/group/sci.math/msg/225dca8f63d0d6ae?hl=en& > > Not changed much, have you? Give me one good reason why I should. Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 04:19 Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote: >> >>>Set theory doesn't claim to subsume all of math. People use it in >>>(almost) every area of math because it works extremely well. >> >>Huh, huh. I use set theory almost nowhere and THAT works extremely well. > > You don't do mathematics. You use calculus in physics. You're lucky that we are pretty much alone in this debate. Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 04:21
Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote: >> >>>Han de Bruijn wrote: >>> >>>>imaginatorium(a)despammed.com wrote: >>>> >>>>>_How_ would you draw a ball from a vase containing an infinite set of >>>>>balls. >>>> >>>>Yaaawn! This has been discussed, at length, as well: >>>> >>>>http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv >>> >>>Why provide a link that is completely irrelevant to the question asked? >> >>Irrelevant? Don't think so. Or did I land on the wrong planet? > > You link to a (misleading) summary of the Vase+Balls thread. Maybe you > could point out what part of that link refers to randomly selecting a > ball from a countably infinite collection? Or did you snip so much > context that even you don't know what you're replying to? Okay. Maybe I simply missed the point .. Han de Bruijn |