An uncountable countable set
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From: Han de Bruijn on 18 Sep 2006 09:57 Mike Kelly wrote: > Han de Bruijn wrote: > >>imaginatorium(a)despammed.com wrote: >> >> >>>_How_ would you draw a ball from a vase containing an infinite set of >>>balls. >> >>Yaaawn! This has been discussed, at length, as well: >> >>http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv > > Why provide a link that is completely irrelevant to the question asked? Irrelevant? Don't think so. Or did I land on the wrong planet? Han de Bruijn
From: Mike Kelly on 18 Sep 2006 09:57 Han de Bruijn wrote: > Mike Kelly wrote: > > > Set theory doesn't claim to subsume all of math. People use it in > > (almost) every area of math because it works extremely well. > > Huh, huh. I use set theory almost nowhere and THAT works extremely well. You don't do mathematics. You use calculus in physics. -- mike.
From: Mike Kelly on 18 Sep 2006 09:59 Han de Bruijn wrote: > Mike Kelly wrote: > > > Han de Bruijn wrote: > > > >>imaginatorium(a)despammed.com wrote: > >> > >> > >>>_How_ would you draw a ball from a vase containing an infinite set of > >>>balls. > >> > >>Yaaawn! This has been discussed, at length, as well: > >> > >>http://huizen.dto.tudelft.nl/deBruijn/grondig/natural.htm#bv > > > > Why provide a link that is completely irrelevant to the question asked? > > Irrelevant? Don't think so. Or did I land on the wrong planet? > > Han de Bruijn You link to a (misleading) summary of the Vase+Balls thread. Maybe you could point out what part of that link refers to randomly selecting a ball from a countably infinite collection? Or did you snip so much context that even you don't know what you're replying to? -- mike.
From: Han de Bruijn on 18 Sep 2006 10:00 Mike Kelly wrote: > Han de Bruijn wrote: > >>Mike Kelly wrote: >> >>>Han.deBruijn(a)DTO.TUDelft.NL wrote: >>> >>>>What I meant to express is that you are about to be parrotting >>>>mainstream arguments, without adding to it much thoughts of >>>>yourself. And that is quite senseless because we have gone >>>>through all this already. >>> >>>Yes, and your position was utterly ripped apart in the very first >>>response to you by David C. Ullrich, and then by several others. You >>>were unable to defend your claim. So, why repeat it as though it were >>>in any way valid? >> >>That's because I did a _honest attempt_ to fit my position into the >>framework of nonstandard analysis (Robinson's theory), which failed. > > Your claim was that *standard* set theory + calculus contradicts > *standard* probability theory. This is untrue. Do you admit it? Of course not. >>Of course it failed. Mainstream mathematicians have never understood >>how infinitesimals work. > > NSA is part of mainstream mathematics. What mathematics have never > understood is why some people are so enarmoured of vigorous handwaving > as a form of mathematical argument. Huh, huh. How cute. Take a look at yourself and your aleph_0s. Han de Bruijn
From: Mike Kelly on 18 Sep 2006 10:01
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. > 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"? -- mike. |