An uncountable countable set
in [Math]
|
Prev: integral problem
Next: Prime numbers
From: Han de Bruijn on 29 Sep 2006 03:14 Virgil wrote: > In article <2e658$451b78ef$82a1e228$7519(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Tony Orlow wrote: >> >>>MoeBlee wrote: >>> >>>>Tony Orlow wrote: >>>> >>>>>Constructivism and Axiomatism are two sides of a coin. They can be >>>>>reconciled in larger framework, I think. >>>> >>>>I don't know what your definition of 'axiomatism' is, but there are >>>>axiomatic systems for constructive mathematics. >>> >>>I dunno. I was responding to Han's comment. I think he means >>>constructive concepts vs. axiomatic declarations. >> >>It's a priorities issue. Do axioms have to dictate what constructivism >>should be like? Should constructivism be tailored to the objectives of >>axiomatics? I think not. > > But if you cannot clearly state what you are assuming/accepting as true, > all you have is a morass of ambiguity. Ambiguity does not necessarily comprise a morass. Han de Bruijn
From: Han de Bruijn on 29 Sep 2006 03:21 Virgil wrote: > In article <cddac$451b7c18$82a1e228$8598(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Virgil wrote: >> >>>In article <c43c$451a2703$82a1e228$4034(a)news1.tudelft.nl>, >>> Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> 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: >>>>>> >>>>>>>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 >>> >>>Correction: >>>mathematics | science | result >>>---------------------------------------------- >>> 0 0 having a chat >>> 0 1 nonsense sciences >>> 1 0 not yet applied maths >>> 1 1 exact sciences >> >>OK. We are getting somewhere. So you believe that science without maths >>is nonsense ? > > I am merely countering your nonsense that math without science is > nonsense. That's what I'm saying all the time. You are contradicting yourself. > According to history, and what can be deduced of prehistory, there was a > good deal of math, at least arithmetic, around long before there was any > science at all. No. Because that "good deal of math" must be considered as scientific. Unlike aleph_0, it helped people to count their cattle and survive. Han de Bruijn
From: Han de Bruijn on 29 Sep 2006 03:38 Virgil wrote: > In article <9fd0$451b7e7b$82a1e228$8977(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Virgil wrote: >> >>>In article <451a8f41(a)news2.lightlink.com>, >>> Tony Orlow <tony(a)lightlink.com> wrote: >> >>>>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. >> >>Crucial question: are those "approximation methods" part of mathematics? >>I'll take Yes or No as a sufficient answer. > > They are a part of the applications of mathematics to things other than > mathematics, so they are marginal. That sounds like a smart answer, but I don't buy it. Again: are those "approximation methods" part of mathematics? Yes or No. Han de Bruijn
From: Han de Bruijn on 29 Sep 2006 03:39 Virgil wrote: > In article <af46f$451b7f3e$82a1e228$9075(a)news1.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >>Tony Orlow wrote: >> >>>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? >> >>Why not? Does Freudian Analysis lead to a technology in a medical sense: >>does it help to cure people from a mental disease? If the answer is yes, >>then IMHO Freudian Analysis may be considered as a science. > > I find myself argeeing with Han on the issue as a whole, though I am > somewhat doubtful of the efficacy of Freudian analysis. So am I. Han de Bruijn
From: stephen on 29 Sep 2006 03:49
Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> So why is it okay to end up with zero balls, when you never remove >> any at all, but it is not okay to end up with zero balls when >> each ball is clearly removed at a definite time? > Why is it not okay to approach the infinite otherwise than via the limit > concept? Applied to a _finite_ sequence of events? > Han de Bruijn Your first sentence has a double negative in it, so I am not sure what you intended to say. It is okay to approach the infinite via the limit concept. Who has ever said otherwise? Stephen |