Xref: utzoo comp.theory:1783 comp.lang.functional:723 Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!zaphod.mps.ohio-state.edu!swrinde!elroy.jpl.nasa.gov!decwrl!deccrl!bloom-beacon!eru!hagbard!sunic!mcsun!ukc!edcastle!aiai!aipna!cstr!rjc From: rjc@cstr.ed.ac.uk (Richard Caley) Newsgroups: comp.theory,comp.lang.functional Subject: Re: do computers believe in real numbers? Message-ID: Date: 3 Apr 91 09:50:56 GMT References: <7197@munnari.oz.au> <91090.154205NN1@awiwuw11.wu-wien.ac.at> <6878@rex.cs.tulane.edu> Sender: news@aipna.ed.ac.uk Organization: Centre for Speech Technology Research Lines: 23 In-reply-to: fs@caesar.cs.tulane.edu's message of 2 Apr 91 16:20:44 GMT In article <6878@rex.cs.tulane.edu>, Frank Silbermann (fs) writes: fs> Also, consider the fact that mathematics fs> has not given us any single notation fs> suitable for expressing _every possible_ fs> computable function over the reals (or even the rationals). Apologies if I am being slow, but if a function is computable does that not imply that it can be denoted in some notational scheme which someone has decided is a reasonable model of `computation' (e.g. TMs, Markov Algorithms or whatever). If `computable' is deleted from the sentance quoted it becomes an obvious tautology, so I must be missing something. BTW: has anyone mentioned Boehm & Cartwright's paper in `Research Topics in Functional Programming'? They argue that the reals should be represnted as functions not as digit sequences for efficiancy reasons(!). (full reference on demand, I don't have it with me). -- rjc@cstr.ed.ac.uk Wandered in from sci.lang to ask dumb questions.