Give me ONE digit position of any real that isn't computable up to that digit position!
in [Math]
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From: FredJeffries on 15 Jun 2010 10:53 On Jun 10, 1:43 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > > 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). Everything is C-infinity. Where's the singularities? Where's the everywhere continuous nowhere differentiable functions? How can George Lucas make those planets with coastlines and mountains in Star Wars? What about Velcro?
From: Transfer Principle on 15 Jun 2010 17:00 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. 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.
From: George Greene on 15 Jun 2010 17:52 On Jun 15, 5:00 pm, Transfer Principle <lwal...(a)lausd.net> wrote: > But there has to be a reason why most mathematicians use > classical analysis and not smooth infinitesimal analysis. No, really, there doesn't. At least not beyond "It's simpler and it was discovered first". If you want more support for THAT reason, read "The Structure of Scientific Revolutions" by Thomas Kuhn. This makes almost as little sense as asking why people use the standard (rather than a non-standard) model of PA; why are they being so unfair to supernatural numbers?
From: Tim Little on 16 Jun 2010 04:45 On 2010-06-13, Leland McInnes <leland.mcinnes(a)gmail.com> wrote: > You can also try http://arxiv4.library.cornell.edu/abs/0805.3307 if > you prefer a little instant gratification from freely available web > sources. That is really quite interesting material. The idea may be old hat to some readers here, but to me that's the first time I've seen the weaker logic used as an enhancement in allowing stronger sets of axioms without contradiction. In hindsight it is obvious. > Then there's "Synthetic Differential Geometry" by A. Kock (available > for download from http://home.imf.au.dk/kock/sdg99.pdf); I haven't got into this one yet, but looking forward to it. - Tim
From: Jesse F. Hughes on 16 Jun 2010 08:14
Tim Little <tim(a)little-possums.net> writes: > On 2010-06-13, Leland McInnes <leland.mcinnes(a)gmail.com> wrote: >> You can also try http://arxiv4.library.cornell.edu/abs/0805.3307 if >> you prefer a little instant gratification from freely available web >> sources. > > That is really quite interesting material. The idea may be old hat to > some readers here, but to me that's the first time I've seen the > weaker logic used as an enhancement in allowing stronger sets of > axioms without contradiction. In hindsight it is obvious. No! No no no no NO! You're supposed to defend ZFC by rejecting Smooth Infinitesimals because they are different than ZFC. Has Walker taught you *nothing* about what it means to be an adherent? Geez. -- Jesse F. Hughes "I think the problem for some of you is that you think you are very smart. I AM very smart. I am smarter on a scale you cannot really comprehend and there is the problem." -- James S. Harris |