An uncountable countable set
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From: Han de Bruijn on 19 Sep 2006 05:24 Mike Kelly wrote: > I'm not suggesting that *no* snipping be done. I'm suggesting that you > don't snip the *relevant* context, so as to not quote people in a > misleading fashion. You have distorted the meaning of several of my > posts in this thread alone. And you seem to be doing it all the time > when I look at other threads you have been involved in. It's simply > dishonest. Geez! I'm filtering from a poster the things *I* find important and *I* want to reply to. And then people find that I'm dishonest? What kind of planet is this? Han de Bruijn
From: Mike Kelly on 19 Sep 2006 05:29 Han de Bruijn wrote: > Mike Kelly wrote: > > > I'm not suggesting that *no* snipping be done. I'm suggesting that you > > don't snip the *relevant* context, so as to not quote people in a > > misleading fashion. You have distorted the meaning of several of my > > posts in this thread alone. And you seem to be doing it all the time > > when I look at other threads you have been involved in. It's simply > > dishonest. > > Geez! I'm filtering from a poster the things *I* find important and *I* > want to reply to. And then people find that I'm dishonest? What kind of > planet is this? > > Han de Bruijn One where it is sometimes necessary to view a sentence in context to understand the meaning? This is not a difficult concept, Han. -- mike
From: Han de Bruijn on 19 Sep 2006 05:29 Mike Kelly wrote: > Han de Bruijn wrote: > >>All naturals do not exist. What is "all"? > > Huh? So some naturals don't exist? What does that mean? How can > something that doesn't exist be a natural number? "All naturals" is undefined, void of meaning. Got it? Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 05:35 Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote: >> >>>Han de Bruijn wrote: >>> >>>>Mike Kelly wrote in response to Tony Orlow: >>>> >>>>>*sigh*. Probabilities are *standard* real numbers between 0 and 1. >>>> >>>>Yes. And infinitesimals are *standard* real numbers in engineering. >>> >>>Engineering is not mathematics. It uses mathematical results. >> >>Sure. And moslems are not praying. Only roman catholics do. > > Bizarre and borderline offensive analogy. Engineering isn't > mathematics, anymore than accounting is mathematics. They both *use* > mathematics. Wrong. They both *create* mathematics as well. I know, because I've been active in both engineering and adminstration. >>>>That's why infinitesimal probabilities will become feasible as soon >>>>as mathematics becomes a science which is compliant with engineering. >>> >>>Mathematics is not a science. What exactly would it mean for it to >>>"become a science compliant with engineering"? >> >>Ah! Mathematics is not a science. So mathematics is not serious at all! >>Why didn't you tell me this before? > > How do you get from "mathematics is not a science" to "mathematics is > not serious"? Time to brush up on your English, Han. How can mathematics be serious, if it is not scientific? Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 05:40
Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote: >> >>>Han.deBruijn(a)DTO.TUDelft.NL wrote: >>> >>>>Mike Kelly wrote: >>>> >>>>>Infinite natural numbers. Tish and tosh. Good luck explaining that idea >>>>>to schoolkids. >>>> >>>>Look who is talking. Good luck explaining alpha_0 to schoolkids. >>> >>>Sure, the theory of infinite cardinals is beyond (most)schoolkids. But >>>this is a bad analogy, because school kids don't need to know about >>>cardinals but they do need to know how to work with natural numbers. My >>>point, if you really missed it, was that Tony's ideas of "infinite >>>natural numbers" don't match up to our "naive" or "intuitive" idea of >>>what numbers should be - how we were taught to do arithmetic in school. >>>I for one don't understand what the hell an "infinite natural number" >>>is. And yet supposedly the advantage of his ideas are that they're more >>>intuitive than a standard formal treatment. >> >>My point is that the pot is telling the kettle that it's black (: de pot >>verwijt de ketel dat ie zwart is). Your aleph_0 is in no way better than >>Tony's "infinite natural number". > > Your analogy is terrible, as usual. > > My point was that Tony's "infinite natural numbers" are not compliant > with everyday arithmetic. Aleph_0 is part of a formalisation that leads > to an arithmetic that works exactly as we expect it to. "... that works exactly as we expect it to". Ha, ha. Don't be silly! Han de Bruijn |