From mboxrd@z Thu Jan 1 00:00:00 1970 X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me X-Spam-Level: X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00,FREEMAIL_FROM autolearn=ham autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,103b407e8b68350b X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2003-02-04 00:42:31 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!cyclone.bc.net!newsfeed.media.kyoto-u.ac.jp!newsfeed01.tsnz.net!news.xtra.co.nz!53ab2750!not-for-mail From: "AG" Newsgroups: comp.lang.ada References: Subject: Re: Anybody in US using ADA ? One silly idea.. X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2800.1106 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2800.1106 Message-ID: Date: Tue, 4 Feb 2003 21:44:22 -0800 NNTP-Posting-Host: 219.88.60.247 X-Complaints-To: newsadmin@xtra.co.nz X-Trace: news.xtra.co.nz 1044348150 219.88.60.247 (Tue, 04 Feb 2003 21:42:30 NZDT) NNTP-Posting-Date: Tue, 04 Feb 2003 21:42:30 NZDT Organization: Xtra Xref: archiver1.google.com comp.lang.ada:33746 Date: 2003-02-04T21:44:22-08:00 List-Id: "Grein, Christoph" wrote in message news:mailman.10.1044267682.3911.comp.lang.ada@ada.eu.org... > > > Do you know, an integer is definitely a real number. > > > > You sure? How about a simple theorem that any two distinct > > real numbers have another real number between them? Either > > this theorem doesn't hold (and the whole math goes out > > the window) or the integers are most definitely not reals. > > > > Which will it be? > > Where is there the contradiction? Integers can be embedded in reals as a subset. Operations available for the type and how they behave. The theorem above was an example. Let's see: F(X, Y) = A such that for any given, finite X and Y where X < Y it produces A that satisfies the requirement that X < A < Y Trivial to do for real numbers. Impossible for integers. Which means that, at least in this respect, integers are not a subset of reals. To be more precise, you could argue that they are a subset or real *values* but that's not the same thing. You could also define an operation F that takes two integers and returns a generic real but that would also mean that integers do not posess a property critical to the definition of the real numbers.