An uncountable countable set
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From: Mike Kelly on 18 Sep 2006 10:03 Han de Bruijn wrote: > Virgil wrote: > > > In article <1158489723.269348.27860(a)e3g2000cwe.googlegroups.com>, > > Han.deBruijn(a)DTO.TUDelft.NL wrote: > > > >>What's wrong with mathematics ?! > > > > Nothing!! > > "Mathematics should be a science" is the answer. Why? -- mike.
From: Mike Kelly on 18 Sep 2006 10:04 Han de Bruijn wrote: > Virgil wrote: > > > As HdB has not been able to counter any of the mainstream arguments to > > the satisfaction of any but himself, they are sufficient. > > Never underestimate the strength of your opponent. > And the influence of 'sci.math' as a free forum. > > Han de Bruijn Channelling James Harris? -- mike.
From: Mike Kelly on 18 Sep 2006 10:05 Han de Bruijn wrote: > Tony Orlow wrote: > > > Mike Kelly wrote: > >> > >> *sigh*. Probabilities are *standard* real numbers between 0 and 1. > > > > *Standard* probabilities are *standard* real numbers from 0 to 1. > > Yes, but according to mainstream mathematics, infinitesimals are _not_. > Hence, in standard mathematics, probabilities cannot be infinitesimals. Right. > Shame! Why? > (Oh well, is non-standard analysis a part of standard mathematics?) Yes. Probability with infinitesimals is not. Did you ever wonder why? Try thinking about it sometime. Maybe you would need to know a little more about rigorous probability theory than you do. -- mike.
From: Ross A. Finlayson on 18 Sep 2006 10:21 Mike Kelly wrote: > Han de Bruijn wrote: > > Tony Orlow wrote: > > > > > Mike Kelly wrote: > > >> > > >> *sigh*. Probabilities are *standard* real numbers between 0 and 1. > > > > > > *Standard* probabilities are *standard* real numbers from 0 to 1. > > > > Yes, but according to mainstream mathematics, infinitesimals are _not_. > > Hence, in standard mathematics, probabilities cannot be infinitesimals. > > Right. > > > Shame! > > Why? > > > (Oh well, is non-standard analysis a part of standard mathematics?) > > Yes. Probability with infinitesimals is not. Did you ever wonder why? > Try thinking about it sometime. Maybe you would need to know a little > more about rigorous probability theory than you do. > > -- > mike. Wow, between any two irrationals there's a rational. I don't know if it's "standard", but a lot of people think the integral calculus is the infinitesimal analysis, and in probability some even use non-standard measure theory, with infinitesimals. Infinitely many infinitesimals are summed to get finite values, that happen to give perfect results. NSA is not very different from standard. That is to say, besides (Robinso(h)nian) "Non-Standard Analysis", there are a variety of other non-standard analyses or analytical treatments. There are no elements in N not in the generic extension, and none in the generic extension not in N. Ross
From: stephen on 18 Sep 2006 10:21
Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: > stephen(a)nomail.com wrote: >> Han de Bruijn <Han.deBruijn(a)dto.tudelft.nl> wrote: >> >>>mueckenh(a)rz.fh-augsburg.de wrote: >> >>>>Representation is number. There is no difference. Numerals have no >>>>"soul". >> >>>Whew! I've never heard someone expressing this fact so lucidly! >> >> So 3/2 is a different number than 6/4? The representations >> differ, and if there is no difference between representation >> and number, then different representations must imply different >> numbers. For that matter 6 birds is a different representation >> of 6 than 6 cars. And 6 birds is a different representation >> of 6 than 6 different birds? How many 6's are there? > Try to understand what equality means. > Han de Bruijn 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? Stephen |