An uncountable countable set
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From: Han de Bruijn on 21 Sep 2006 06:30 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. > 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. > 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 :-) Han de Bruijn
From: Han de Bruijn on 21 Sep 2006 06:35 stephen(a)nomail.com wrote: > Han.deBruijn(a)dto.tudelft.nl wrote: > >>stephen(a)nomail.com wrote: > >>>Is sqrt(2) a number? > >>Yes. > > Really?? Below is the definition you have apparently embraced: > >> *The number* is each of its representations. The number 3 >> 1) either is realized by a fundamental set like the following >> fundamental set of 3: >> {III, Dik, {a,b,c}, {father, mother, child}, {sun, moon, earth}, >> ...} >> 2) or is completely determined by a series of digits >> like 3.000000 or 3.00 or 3 or 3/1 or 6/2. (6/2 can also be interprtede >> as an exercise.) > > So what is a fundamental set of sqrt(2)? > > What series of digits completely determines sqrt(2)? > > You are in disagreement with WM, who has clearly stated > that sqrt(2), pi, e and all the irrationals are not numbers. I think that you are babbling, but before saying so, I shall first read what WM actually says about it. Han de Bruijn
From: Han de Bruijn on 21 Sep 2006 07:20 Mike Kelly wrote [ snipping all of the awful nesting ]: > Tony Orlow wrote [ .. snip .. ]: > >>which led him to say, "Precisely!". Hmmm, I don't think it's an English >>problem. > > Well apparently neither of you have any idea what my point was. > Hopefully I have clarified it now. That's funny. So the "English problem" is now between two native English speakers and a Dutchman. Who is misunderstanding who ... Han de Bruijn
From: Dik T. Winter on 21 Sep 2006 08:03 In article <1158294172.235202.174240(a)h48g2000cwc.googlegroups.com> imaginatorium(a)despammed.com writes: > > Dik T. Winter wrote: .... > > > Somthing like that. In my opinion, when you have a set of objects, two > > > operations (+ and *) of which one is distributive over the other, > > > you can talk about numbers. > > This seems an odd definition, since it means that anything that forms a > ring would count as numbers: polynomials, matrices, and goodness knows > what. Yes, I thought about that later when I had already posted. You would like to omit the stuff you mention, and also Boolean algebra's. On the other hand, I would like to keep in things like the 10-adics (although they are the direct sum of the 2-adics and the 5-adics). -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/
From: Dik T. Winter on 21 Sep 2006 08:11
In article <1158311965.841357.58540(a)d34g2000cwd.googlegroups.com> mueckenh(a)rz.fh-augsburg.de writes: > Dik T. Winter schrieb: > > > Still you have not answered my question: "what law is he using"? > > I improved this translation already to "truth" > > > On the > > other hand, you should familiarise yourself with the meaning of the > > English word "axiom". One of the meanings from Merriam-Webster: > > an established rule or principle or a self-evident truth > > Note the latter part, which (I think) entirely conforms with Cantor's > > "Grundsatz". > > The latter part does conform with Cantor's but not with the meaning of > "axiom" in modern mathematics. Webster obviously was not a modern > mathematician. In modern mathematics there are no self-evident truths. There are the axioms that are the basic material to work with and the theorems that follow from them. In that sense, Cantor's Grundsatz is completely equivalent with an axiom as used in modern mathematics. And so, translating it with "axiom" is neither wrong, nor misleading. > > > > Although I disagree that > > > > changing them leads to rubbish. > > > > > > because you have not yet understood what Cantor's truths are. > > > > Educate me. What are they? Pray provide sources. But your rubbish > > is not my rubbish... > > Cantor's truths are self-evident truths which cannot be changed > arbitrarily in contrast to the axioms of modern set theory. Yeah, whatever. Is this a reply to my question? -- dik t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131 home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/ |