Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!news.mixmin.net!feeds.phibee-telecom.net!newsfeed.xs4all.nl!newsfeed4a.news.xs4all.nl!xs4all!newsgate.cistron.nl!newsgate.news.xs4all.nl!post.news.xs4all.nl!not-for-mail Return-Path: X-Original-To: python-list@python.org Delivered-To: python-list@mail.python.org X-Spam-Status: OK 0.120 X-Spam-Level: * X-Spam-Evidence: '*H*': 0.76; '*S*': 0.00; 'subject:set': 0.09; 'cc:addr:python-list': 0.11; 'from:addr:rosuav': 0.16; 'from:name:chris angelico': 0.16; 'non-integers': 0.16; 'wrote:': 0.18; 'cc:addr:python.org': 0.22; 'adds': 0.24; 'integer': 0.24; 'cc:2**0': 0.24; 'least': 0.26; 'header:In-Reply-To:1': 0.27; 'is?': 0.30; 'message-id:@mail.gmail.com': 0.30; 'that.': 0.31; 'subject:numbers': 0.31; 'subject:size': 0.31; 'way?': 0.31; 'figure': 0.32; 'subject:the': 0.34; 'subject: (': 0.35; 'subject:with': 0.35; "can't": 0.35; 'but': 0.35; 'received:google.com': 0.35; 'there': 0.35; 'sequence': 0.36; "didn't": 0.36; 'easily': 0.37; 'represent': 0.38; 'pm,': 0.38; 'even': 0.60; 'continued': 0.60; 'numbers': 0.61; 'real': 0.63; 'series': 0.66; 'mar': 0.68; 'square': 0.74; 'url:fibonacci': 0.84; 'to:none': 0.92 DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:date:message-id:subject:from:cc :content-type:content-transfer-encoding; bh=Pc0fzRu77Qosg/usToDLfVbutWhhmA+oS66dV6Pusd0=; b=Y6N4DOEQn6SemiC5MULf7RtlgAIe7V/tY1vkOup9kyXVX3oitkFCwnNyvXFgMvxUIM Iq8eXB18NG7vuRoXI4fB8yHId5TehNGXb9/90d9/ueUlLhTMtsTsfrQkYU1ljUr3GVi4 6Uh26yCfC7nyFMzg024bLKCNtKA8KUB9WwwKeVlBHBJ5ZJeO5qaLyvirrhPfXBRLgjcu vUKt2WrcEDH4E34G4aWKsg9MOPHgnGM24ASrGjN1jjXpesYcdHOevE2a2wJmwuHPsz2Z 3br1pOVP86DnzVB+xkDr1Le9lzK6vOyAtcc4A4fxLy9+ybfcj+PylQ6hOwkbnyd1f9cY cyfA== MIME-Version: 1.0 X-Received: by 10.69.25.69 with SMTP id io5mr14853707pbd.22.1393904786012; Mon, 03 Mar 2014 19:46:26 -0800 (PST) In-Reply-To: <59dd57ad-39b0-4c71-a58e-b4ae6517b385@googlegroups.com> References: <8e4c1ab1-e65d-483f-ad9d-6933ae2052c3@googlegroups.com> <85r478bv99.fsf_-_@benfinney.id.au> <53153e66$0$24931$e4fe514c@dreader36.news.xs4all.nl> <59dd57ad-39b0-4c71-a58e-b4ae6517b385@googlegroups.com> Date: Tue, 4 Mar 2014 14:46:25 +1100 Subject: Re: Working with the set of real numbers (was: Finding size of Variable) From: Chris Angelico Cc: "python-list@python.org" Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable X-BeenThere: python-list@python.org X-Mailman-Version: 2.1.15 Precedence: list List-Id: General discussion list for the Python programming language List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Newsgroups: comp.lang.python Message-ID: Lines: 19 NNTP-Posting-Host: 2001:888:2000:d::a6 X-Trace: 1393904790 news.xs4all.nl 2833 [2001:888:2000:d::a6]:37555 X-Complaints-To: abuse@xs4all.nl Xref: csiph.com comp.lang.python:67635 On Tue, Mar 4, 2014 at 2:13 PM, Rustom Mody wrote: >> But it's a far cry from "all real numbers". Even allowing for >> continued fractions adds only some more; I don't think you can >> represent surds that way. > > See > > http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/cfINTRO.html= #sqrts That's neat, didn't know that. Is there an efficient way to figure out, for any integer N, what its sqrt's CF sequence is? And what about the square roots of non-integers - can you represent =E2=88=9A=CF=80 that w= ay? I suspect, though I can't prove, that there will be numbers that can't be represented even with an infinite series - or at least numbers whose series can't be easily calculated. ChrisA