An uncountable countable set
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From: Virgil on 27 Sep 2006 00:08 In article <1159328002.537349.291560(a)e3g2000cwe.googlegroups.com>, imaginatorium(a)despammed.com wrote: > David R Tribble wrote: > > Tony Orlow wrote: > > > For the sake of this argument, we can talk about infinite reals, of > > > which infinite whole numbers are a subset. > > > > What are these "infinite reals" and "infinite whole numbers" that you > > speak of so much? > > > > If you've got a set containing the finite naturals and the "infinite > > naturals", how do you define it? N is the set containing 0 and all > > of its successors, so what is your set? > > Oh, I should think it's the same, only if you keep an open mind, and > try harder. (How'm I doing, Tony?) > > Brian Chandler > http://imaginatorium.org But TO's mind is so open it stays empty.
From: Han de Bruijn on 27 Sep 2006 03:05 Tony Orlow wrote: > Han de Bruijn wrote: > >> Tony Orlow wrote: >> >>> Math=Science? >> >> Definitely, yes! > > George Boole seemed to think so. I think many have. Would you say that's > about equivalent to, "a little physics would be no idleness in > mathematics"? Indeed. Han de Bruijn
From: Han de Bruijn on 27 Sep 2006 03:23 Virgil wrote: > In article <6e5c2$4518da26$82a1e228$6365(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Tony Orlow wrote: >> >>>Math=Science? >> >>Definitely, yes! > > Only if science is a subset of mathematics. Science is not a subset of mathematics. Neither is mathematics a subset of science nowadays. If 1 = yes and 0 = no : mathematics | science | result ------------------------------ 0 0 having a chat 0 1 soft sciences 1 0 nonsense maths 1 1 exact sciences Han de Bruijn
From: Han de Bruijn on 27 Sep 2006 03:30 Virgil wrote: >>Han de Bruijn wrote: >> >>>Tony Orlow wrote: >>> >>>>Han de Bruijn wrote: >>>> >>>>>I may be rude sometimes, but I never get _personal_ by calling somebody >>>>>an "idiot" or a "crank". Tony's "babbling" translates with Euroglot as >>>>>"babbelen" in Dutch, which is a word I can use here in the conversation >>>>>with my collegues without making them very angry (if I say "volgens mij >>>>>babbel je maar wat"). But, of course, I cannot judge the precise impact >>>>>of the word in English. Apologies if it is heavier than I thought. >>>> >>>>Do you have the saying, "Shallow brooks babble, and still waters run >>>>deep"? I figured you picked up the usage from this forum, actually. >>>>It's meant, in English, to mean you aren't making any sense. :) >>> >>>I have talked to my collegues and they have told me that "babbling" in >>>English indeed has a meaning which is somewhat different from "babbelen" >>>in Dutch. It is more like our "lallen", to be translated in English as >>>"talking while you are drunk". Is that correct ? >> >>Yes, or just with an inherently incoherent mind. >> >>>"Babbelen" in Dutch is more like "having a nice chat". It's not that it >>>doesn't make any sense, but it's not very deep either. It's more social >>>than intellectual. > > In the biblical story of the Tower of Babel, the tower builder's speech > becomes incomprehensible to each other, and, at least in English, much > of that meaning remains in the word "babble". Ah! Goes back to the bible ... > The sounds babies make before they have learned to talk is called > 'babbling'. Hey, how nice! That's called "brabbelen" in Dutch, with an "r" added. Han de Bruijn
From: Han de Bruijn on 27 Sep 2006 03:31
Virgil wrote: > In article <45193e6f(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >>Han de Bruijn wrote: >> >>>Tony Orlow wrote: >>> >>>>Virgil wrote: >>>> >>>>>Mathematicians know better. >>>> >>>>Define "better". Those that work in various areas of science share a >>>>notion which defines science. Theories which have no means of >>>>verification are not science, but philosophy. In mathematics, >>>>verification really consists of corroboration by other means, >>>>agreement between different approaches. In science, where you find a >>>>contradiction with your theory, it needs revision. So, the scientific >>>>approach to mathematics requires some criterion for universal >>>>consistency, as measured by the predictions of the various theories >>>>that comprise it. Where two theories collide, one or both is in error. >>>>I think that's better. >>> >>>Precisely ! In mathematics, there are contradictory approaches, such as >>>constructivism (Brouwer) against axiomatism (Hilbert). Its practicioners >>>are asked to be "nice" to each other and to "reconciliate" the different >>>points of view, which turns out to be a hopeless task. Such a situation >>>would be unthinkable if mathematics aimed to be a science. >> >>Well, Han, I'm not sure I agree with the statement that reconciliation >>is hopeless. Is it hopeless to reconcile the wave nature of elementary >>entities with their particle nature? > > It is close to hopeless to expect those who reject the law of the > excluded middle (constructionists) and those who insist on it > (formalists) to agree. That's what I mean. Han de Bruijn |