Give me ONE digit position of any real that isn't computable up to that digit position!
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From: Alan Smaill on 11 Jun 2010 07:12 Transfer Principle <lwalke3(a)lausd.net> writes: > Still, McInnes has started the type of discussion > that I'd like to see. The response I'd like to > see is one which defends classical analysis > against these smooth infinitesimals -- and I mean > something more like "Smooth infinitesimals are bad > because they contradict LEM" than "There are no > nonzero infinitesimals, and anyone who thinks so > is a --" (five-letter insult). Why on earth would you like to see that? -- Alan Smaill
From: Aatu Koskensilta on 12 Jun 2010 11:24 Transfer Principle <lwalke3(a)lausd.net> writes: > The response I'd like to see is one which defends classical analysis > against these smooth infinitesimals This idea, that classical analysis needs defending against smooth infinitesimals, is bizarre. -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Aatu Koskensilta on 12 Jun 2010 11:27 MoeBlee <jazzmobe(a)hotmail.com> writes: > On Jun 10, 3:43�pm, Transfer Principle <lwal...(a)lausd.net> wrote: > >> the vast majority of posters who do mention infinitesimals are >> criticized for doing so. > > I love infinitesimals. I love non-standard analysis. I like smooth infinitesimal analysis better (for various reasons). Let's fight! -- Aatu Koskensilta (aatu.koskensilta(a)uta.fi) "Wovon man nicht sprechan kann, dar�ber muss man schweigen" - Ludwig Wittgenstein, Tractatus Logico-Philosophicus
From: Jesse F. Hughes on 12 Jun 2010 11:34 Aatu Koskensilta <aatu.koskensilta(a)uta.fi> writes: > MoeBlee <jazzmobe(a)hotmail.com> writes: > >> I love infinitesimals. I love non-standard analysis. > > I like smooth infinitesimal analysis better (for various reasons). Let's > fight! There are no nonzero infinitesimals, and anyone who thinks so is a five-letter insult. -- "Is that possible? Could it be that easy? No way. [...] There must be a mistake. Right? "But I am the top mathematician in the world." -- James S. Harris
From: Jesse F. Hughes on 15 Jun 2010 17:14
Transfer Principle <lwalke3(a)lausd.net> writes: > On Jun 12, 8:24 am, Aatu Koskensilta <aatu.koskensi...(a)uta.fi> wrote: >> Transfer Principle <lwal...(a)lausd.net> writes: >> > The response I'd like to see is one which defends classical analysis >> > against these smooth infinitesimals >> This idea, that classical analysis needs defending against smooth >> infinitesimals, is bizarre. > > But there has to be a reason why most mathematicians use > classical analysis and not smooth infinitesimal analysis. Perhaps a matter of taste? Perhaps because their studies are more likely to include classical analysis than smooth infinitesimal analysis? > I thought the fact that the latter contradicts the Law of > the Excluded Middle was one reason to reject it. If not, > then I'd like to see some of the real reasons that the > classical analyis is more prevalent -- and once again, > without the use of five-letter insults. You have a really odd view of how mathematicians approach their subject. I personally have never met a mathematician who claimed to "reject" a branch or theory of mathematics. The closest I came was a logician who believed that only finite sets "really" existed, but his background was more philosophical than mathematical. (And, indeed, this sort of philosophical dispute is, in my experience, *very* rare among knowledgeable folk.) -- "Witty adolescent banter relies highly on the use of 'whatever.' Anyone out of high school forced to watch more than an hour of 'Laguna Beach' might possibly feel the urge to beat themselves about the head with a large stick." -- NY Times on an MTV reality show |