An uncountable countable set
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From: Han de Bruijn on 19 Sep 2006 04:28 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. >>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? Why am I talking with you anyway? Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 04:42 stephen(a)nomail.com wrote: > Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > >>Try to understand what equality means. > > That does not seem to be an answer. Your position is > that "represenation is number". According to you there > is no difference between a number and its representation. > "3/2" is a representation. It is different than "6/4". > Or does your definition of "equality" somehow allow for > different strings to be equal? Read the response by WM. I cannot improve on it. Han de Bruijn
From: Mike Kelly on 19 Sep 2006 04:49 Han de Bruijn wrote: > 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 .. 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. -- mike.
From: Han de Bruijn on 19 Sep 2006 04:52 MoeBlee wrote: > Han de Bruijn wrote: > >>MoeBlee wrote: >> >>>Tony Orlow wrote: >>> >>>>Unbounded but finite may >>>>be considered potentially, but not actually, infinite. >>> >>>That will be jiffy, once you give axioms and/or our definitions for >>>'potentially infinite' and 'actual infinite'. Until then, it's pure >>>handwaving. >> >>Come on, Moeblee, don't be silly! Let Google be your friend! > > I'm well aware of the notions of 'potential infinity' and 'actual > infinity' that go back through at least a couple thousand years of > philosophy and philosophy of mathematics. But to use those notions in Here comes: > an axiomatic mathematics requires either defining the terms > 'potentially infinite' and 'actually infinite' in the axiomatic theory > or taking them as primitive and giving axioms for them in the axiomatic > theory. So far, that has not been done in this thread or in any other > thread I've happened to read. Now look what WM says, elsewhere in this thread: > No. Just this is the point! The series 1 + 1/2 + 1/4 + ... is 2 (or at > least as close to 2 as we like), not by definition and not by any > axiom, but by rational thought. And the same kind of extrapolation is > appropriate if we investigate the infinite, be it the sequence 1/n or > the "bijection" N <--> Q. Let's repeat the essential phrase in capital letters: NOT BY ANY AXIOM, BUT BY RATIONAL THOUGHT. > Meanwhile, rather than direct you to an Internet search, I recommend > 'The Philosophy Of Set Theory' by Mary Tiles for more about 'potential > infinity' and 'actual infinity' and debates through history about > infinity. Han de Bruijn
From: Han de Bruijn on 19 Sep 2006 04:54
Randy Poe 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. > > I think I was 10 when I saw the proof that the rationals are > countable, and first saw the notation "aleph_0". I don't remember > having a problem with it. The bad news is that you still have no problem with the things you learned as a child. Guess you still believe in Santa Claus as well? Han de Bruijn |