An uncountable countable set
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From: Han de Bruijn on 18 Sep 2006 07:10 Aatu Koskensilta wrote: > Tony Orlow wrote: > >> Do you think he would have disagreed with you, Aatu? > > I think there's much I disagree about with Virgil. In particular his > conception of what mathematics is about seems extremely wrongheaded. Virgil thinks that mathematics is not a science. What do you think? Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:18 Mike Kelly wrote: > Tony Orlow wrote: >>The agreement that I think Han and I came to in "Calculus XOR >>Probability" was that such probabilities are infinitesimal. > > Probabilities are never infinitesimal. They are real numbers between 0 > and 1. Infinitesimals in engineering (not in Robinson's nonstandard analysis) are real numbers as well. So here goes ... Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:27 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. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:32 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. That's why infinitesimal probabilities will become feasible as soon as mathematics becomes a science which is compliant with engineering. Han de Bruijn
From: Han de Bruijn on 18 Sep 2006 07:36
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. Han de Bruijn |