Path: csiph.com!v102.xanadu-bbs.net!xanadu-bbs.net!goblin3!goblin2!goblin.stu.neva.ru!newsfeed.xs4all.nl!newsfeed1.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 0.048 X-Spam-Evidence: '*H*': 0.90; '*S*': 0.00; '-10': 0.09; 'subject:set': 0.09; 'cc:addr:python-list': 0.11; '->': 0.16; '-1,': 0.16; 'bend': 0.16; 'infinity': 0.16; 'infinity,': 0.16; 'to:addr:pearwood.info': 0.16; 'to:addr:steve+comp.lang.python': 0.16; "to:name:steven d'aprano": 0.16; 'wrote:': 0.18; 'wed,': 0.18; '(in': 0.22; 'cc:addr:python.org': 0.22; 'math': 0.24; 'cc:2**0': 0.24; 'header:In-Reply-To:1': 0.27; 'chris': 0.29; 'am,': 0.29; 'message-id:@mail.gmail.com': 0.30; 'towards': 0.31; "d'aprano": 0.31; 'steven': 0.31; 'subject:numbers': 0.31; 'subject:size': 0.31; 'maybe': 0.34; 'subject:the': 0.34; 'subject: (': 0.35; 'subject:with': 0.35; 'received:209.85': 0.35; 'but': 0.35; 'received:google.com': 0.35; 'there': 0.35; 'two': 0.37; 'received:209': 0.37; 'rather': 0.38; 'itself': 0.39; 'negative': 0.60; 'back': 0.62; 'series': 0.66; 'mar': 0.68; '10000': 0.68; '(is': 0.84; 'buzz': 0.84; 'increasingly': 0.84; 'universe': 0.84; 'concluded': 0.91 X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:mime-version:in-reply-to:references:from:date :message-id:subject:to:cc:content-type; bh=VSxn3B9DNo5SZNL3TLhryfCO2RH1gd0VfVfb0wvwYeg=; b=RYmRCE7HNJZlpz5GfYDZLZkkZA2D4U/cwM/MDVD5r9mZR2M44FHLlzeJwQujn14N3Q XHW2pqULXZ2Z/KyaJeq083Ghj5Hktvx8FVWpSVavsiptdqFeQqqVIo7jMjoCq121Gwpr aZIQpePOJxDbIQUUEJyiVCzAi4EBAIkgFGBcgM5/+uyuQDx9WUDz36g8NZW16RIvriVu TtV7abGP/Z2KowOgt0fStpVpFyY4hKHov+dOqFNHmGvpGlQmHIH9A+sL8Icnd8cB3UpF gyoFQA5DxsGNLWRLT3pURam8malnum1pNloy6eK5SP2KfK6adIyA3zxBWSKAQZzivHRM +yGQ== X-Gm-Message-State: ALoCoQmpWcgh9NUNw21gxT2zYF3e+HdU1CshdRd1jSdkcvx694st3Oze2f9pN3xsIpwYNliKqG+L X-Received: by 10.60.135.226 with SMTP id pv2mr1573772oeb.62.1394042602262; Wed, 05 Mar 2014 10:03:22 -0800 (PST) MIME-Version: 1.0 In-Reply-To: <53176225$0$29987$c3e8da3$5496439d@news.astraweb.com> References: <8e4c1ab1-e65d-483f-ad9d-6933ae2052c3@googlegroups.com> <53153e66$0$24931$e4fe514c@dreader36.news.xs4all.nl> <531688b1$0$25064$e4fe514c@dreader37.news.xs4all.nl> <53169cd9$0$2923$c3e8da3$76491128@news.astraweb.com> <5316d7a0$0$2923$c3e8da3$76491128@news.astraweb.com> <53176225$0$29987$c3e8da3$5496439d@news.astraweb.com> From: Chris Kaynor Date: Wed, 5 Mar 2014 10:03:02 -0800 Subject: Re: Working with the set of real numbers (was: Finding size of Variable) To: "Steven D'Aprano" Content-Type: multipart/alternative; boundary=047d7b4142c61c246404f3dfd69a Cc: "python-list@python.org" 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: 57 NNTP-Posting-Host: 2001:888:2000:d::a6 X-Trace: 1394043041 news.xs4all.nl 2888 [2001:888:2000:d::a6]:39702 X-Complaints-To: abuse@xs4all.nl Xref: csiph.com comp.lang.python:67864 --047d7b4142c61c246404f3dfd69a Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable On Wed, Mar 5, 2014 at 9:43 AM, Steven D'Aprano < steve+comp.lang.python@pearwood.info> wrote: > At one time, Euler summed an infinite series and got -1, from which he > concluded that -1 was (in some sense) larger than infinity. I don't know > what justification he gave, but the way I think of it is to take the > number line from -=E2=88=9E to +=E2=88=9E and then bend it back upon itse= lf so that there > is a single infinity, rather like the projective plane only in a single > dimension. If you start at zero and move towards increasingly large > numbers, then like Buzz Lightyear you can go to infinity and beyond: > > 0 -> 1 -> 10 -> 10000 -> ... =E2=88=9E -> ... -10000 -> -10 -> -1 -> 0 > This makes me think that maybe the universe is using ones or two complement math (is there a negative zero?)... Chris --047d7b4142c61c246404f3dfd69a Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable

= On Wed, Mar 5, 2014 at 9:43 AM, Steven D'Aprano <<= a href=3D"mailto:steve+comp.lang.python@pearwood.info" target=3D"_blank">st= eve+comp.lang.python@pearwood.info> wrote:
At one time, Euler summed an infinite series and got -1, from = which he
concluded that -1 was (in some sense) larger than infinity. I don't kno= w
what justification he gave, but the way I think of it is to take the
number line from -=E2=88=9E to +=E2=88=9E and then bend it back upon itself= so that there
is a single infinity, rather like the projective plane only in a single
dimension. If you start at zero and move towards increasingly large
numbers, then like Buzz Lightyear you can go to infinity and beyond:

0 -> 1 -> 10 -> 10000 -> ... =E2=88=9E -> ... -10000 -> -= 10 -> -1 -> 0

This makes me think that ma= ybe the universe is using ones or two complement math (is there a negative = zero?)...

Chris
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