An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: Virgil on 27 Sep 2006 15:48 In article <451a8da0(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <45193afa(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > > > >> Virgil wrote: > >>> In article <45189e62(a)news2.lightlink.com>, > >>> Tony Orlow <tony(a)lightlink.com> wrote: > >>> > >>>> Virgil wrote: > >>>>> In article <45187864(a)news2.lightlink.com>, > >>>>> Tony Orlow <tony(a)lightlink.com> wrote: > >>>>> > >>>>>> Han de Bruijn wrote: > >>>>>>> Tony Orlow wrote: > >>>>>>> > >>>>>>>> Mike Kelly wrote: > >>>>>>>> > >>>>>>>>> Han de Bruijn wrote: > >>>>>>>>> > >>>>>>>>>> Mike Kelly wrote: > >>>>>>>>>> > >>>>>>>>>>> Han de Bruijn wrote: > >>>>>>>>>>> > >>>>>>>>>>>> Mike Kelly wrote: > >>>>>>>>>>>> > >>>>>>>>>>>>> What the hell are you talking about? Arguing with someone who > >>>>>>>>>>>>> can't > >>>>>>>>>>>>> speak English is getting aggravating. > >>>>>>>>>>>> My English is much better than your Dutch. > >>>>>>>>>>> So what? Your English is still too poor for this discussion to be > >>>>>>>>>>> fruitful. > >>>>>>>>>> Still don't get the point, huh? > >>>>>>>>>> > >>>>>>>>>> You are lacking even the most elementary form of politeness. It's > >>>>>>>>>> very > >>>>>>>>>> impolite to cut of a discussion with somebody from a foureign > >>>>>>>>>> country - > >>>>>>>>>> somebody who is doing his best to communicate with you - only > >>>>>>>>>> because > >>>>>>>>>> you are obviously superior in expressing your thoughts within your > >>>>>>>>>> own > >>>>>>>>>> mother's tongue. > >>>>>>>>> You're a very rude person yourself, Han. I generally don't feel the > >>>>>>>>> need to be civil to those who won't reciprocate. > >>>>>>>> I don't think I have ever found Han to be rude, except when he > >>>>>>>> referred to my "babbling" recently. Ahem. But anyway, while we > >>>>>>>> disagree on the actuality of any infinity, we have the open mind of > >>>>>>>> spirited debate, and feel no need to get nasty. > >>>>>>> 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. :) > >>>>>> > >>>>>>>> Furthermore, I have never had any trouble understanding what Han is > >>>>>>>> saying, except where he is using some mathematical construct with > >>>>>>>> which I am not familiar. His English is not bad, and blaming your > >>>>>>>> disagreement on his inability to communicate is kind of low. > >>>>>>> Thank you very much, Tony, for this sort of defense. > >>>>>> My pleasure. It seemed like a vacuous excuse. I get pretty sick of > >>>>>> those > >>>>>> diversionary tactics. > >>>>>> > >>>>>>>> So, let's engage in lively debate, and maintain our civility, while > >>>>>>>> chopping each other's arguments to pieces. Of course, this can only > >>>>>>>> happen if we don't consider our arguments to be part of our anatomy. > >>>>>>>> Otherwise, it gets personal. > >>>>>>>>>>> You are misinterpreting virtually all my posts. You claim that > >>>>>>>>>>> you're > >>>>>>>>>>> not dishonest so I have to conclude you're simply incapable of > >>>>>>>>>>> comprehending written English. This makes this whole subthread > >>>>>>>>>>> pointless. > >>>>>>>>>> I have only this kind of trouble with _you_ and nobody else on the > >>>>>>>>>> web. > >>>>>>>>> Really? You've never had anybody else other than me complain that > >>>>>>>>> you > >>>>>>>>> misinterpret their posts? I suppose I must have hallucinated dozens > >>>>>>>>> of > >>>>>>>>> posts I've seen of just that, then. > >>>>>>>>> > >>>>>>>>> You've never had anyone other than me struggling to understand what > >>>>>>>>> the > >>>>>>>>> devil you mean by your broken English? I must have hallucinated, > >>>>>>>>> for > >>>>>>>>> example, "A little physics would be no idleness in mathematics", > >>>>>>>>> then > >>>>>>>>> :)? > >>>>>>>> Well, that's a difficult type of quote. Han - I wouldn't mind > >>>>>>>> working > >>>>>>>> on exactly how you want to say that in English, if you like. :) > >>>>>>> Uhm, since litteraly everybody is complaining ... Let it be an > >>>>>>> encrypted > >>>>>>> message then :-) > >>>>>> Well, it seems to me that perhaps you're saying something like, "Those > >>>>>> with their heads in the abstract should keep their feet in the > >>>>>> concrete", though that sounds a little funny. > >>>>>> > >>>>>> Math=Science? > >>>>> Scientists, particularly those in the sciences most dependent on > >>>>> mathematics, tend to think that all mathematics is, or should be, a > >>>>> subservient to their particular fragment of science. > >>>>> > >>>>> 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. > >>> TO mistakes misapplication of mathematics, which is an error by > >>> scientists, as an error of the mathematics. > >>> > >> That's not what I said, and you know it. > > > > When an application of mathematics to physics, or some other science, > > does not predict what actually is observed in that science, why does TO > > insist the problem is inherent in the mathematics alone and not in the > > i
From: Tony Orlow on 27 Sep 2006 15:55 imaginatorium(a)despammed.com wrote: > Tony Orlow wrote: >> Randy Poe wrote: >>> Tony Orlow wrote: >>>> Randy Poe wrote: >>>>> Tony Orlow wrote: >>>>>> Randy Poe wrote: >>>>>>> Tony Orlow wrote: >>>>>>>> Virgil wrote: >>>>>>>>> Tony Orlow <tony(a)lightlink.com> wrote: > > ... much, leading nowhere. > > Tony, > > Would you care to answer me some questions? No tricks or anything, just > something about what we would call graphs in the x-y plane? > > Here's a starter: > > Consider a (notional, theoretical, mathematical, not physical) x-y > plane. That is, an area in which there is a point (0,0) in some > particular place, an x-axis, y-axis, and points are identified by > coordinates x and y, using (in normal maths) real values for these > coordinates. Consider (for convenience) that this plane is embedded in > a notional graphics application, with a "Fill" function. So if we draw > the circle x^2 + y^2 = 49 (centre origin, (constant! Zick, be quiet!) > radius 7), then click with the Fill function on the point (2,1), it > fills the circle, and no paint spills outside that radius 7. > > Now suppose we have the graphs of x=2 and x=5. Vertical lines, > extending up and down without limit. Suppose we click with the Fill > function on the point (3, 4), what would you say happens? Obviously > paint fills the vertical strip of width 3. Would you say that any paint > was able to "spill" around the (nonexistent!) "top" of either of the > graphs, and somehow fill more of the plane than this strip, or would > you say we just get a (vertically) unbounded strip of blue? (Goddabe > blue!) > > If you care to answer, I'd like to ask one or two more similar > questions. If you don't want to bother, please say, and I will save my > time. > > Brian Chandler > http://imaginatorium.org > I'd have to agree that it would fill the strip only. Proceed, but it would be nice to know the context of the question. Tony
From: Virgil on 27 Sep 2006 15:55 In article <451a8f41(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.com> wrote: > Virgil wrote: > > In article <45193e6f(a)news2.lightlink.com>, > > Tony Orlow <tony(a)lightlink.com> wrote: > >> 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. > > > > If neither can appreciate the other's point, perhaps. Some christians > get along quite well with some muslims. Only by agreeing to disagree. > > The question boils down to whether 0^0 is 1. 0^0 is, in any particular context, what it is defined to be. There are contexts in which it is more useful to have it mean 1 and others where it is more useful to have it mean 0. > > > >> There is confusion about my "definition" of infinitesimals, because I > >> can see the validity both in nilpotent infinitesimals and in those that > >> are further infinitely divisible. > > > > Until TO can come up with an axiom system which simultaneously allows > > his infinitesimals to be both nilpotent and not, he is in trouble. > > > > For purposes of measure on the finite scale, infinitesimals can be > considered nilpotent. That's all. Do you disagree? I disagree that scale changes can convert between zero and non-zero. There are approximation methods is which products of small quantities are regarded as negligible in comparison to the quantities themselves, but they are always just approximations.
From: Tony Orlow on 27 Sep 2006 15:58 Virgil wrote: > In article <451a891f(a)news2.lightlink.com>, > Tony Orlow <tony(a)lightlink.com> wrote: > >> 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: >>>> >>>>> 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 ? >>>> >>>> "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. >>>> >>>>> Math=Science? >>>> Definitely, yes! >>> Only if science is a subset of mathematics. >> There is no science without mathematics, if that's what you mean. > > There are certainly areas of study which call themselves sciences which > are at most peripherally mathematical, such as much of psychology. Psychology (and I've studied it a bit) is only a science to the extent that it employs analysis. Most cognitive science uses at least statistics in order to establish any kind of certainty in its findings. I don't consider Freudian Analysis to be science. Do you?
From: Virgil on 27 Sep 2006 15:58
In article <451a8ff5(a)news2.lightlink.com>, Tony Orlow <tony(a)lightlink.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? > > > > The very same, with no restriction of finiteness. Any T-riffic number > has successor. :) So TO's set contains more members that it contains? N is either limited to containing only finite members or not so limited, but cannot be both simultaneously. Unless there are no infinite naturals. |