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=-2.9 required=5.0 tests=BAYES_00,MAILING_LIST_MULTI autolearn=unavailable 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 01:22:22 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!cyclone.bc.net!newsfeed.media.kyoto-u.ac.jp!newsfeed.icl.net!newsfeed.fjserv.net!proxad.net!freenix!enst.fr!not-for-mail From: "Grein, Christoph" Newsgroups: comp.lang.ada Subject: Re: Anybody in US using ADA ? One silly idea.. Date: Tue, 4 Feb 2003 10:13:59 +0100 (MET) Organization: ENST, France Message-ID: Reply-To: "Grein, Christoph" , "comp.lang.ada mail to news gateway" NNTP-Posting-Host: marvin.enst.fr Mime-Version: 1.0 Content-Type: TEXT/plain; charset=us-ascii X-Trace: avanie.enst.fr 1044350542 29530 137.194.161.2 (4 Feb 2003 09:22:22 GMT) X-Complaints-To: usenet@enst.fr NNTP-Posting-Date: Tue, 4 Feb 2003 09:22:22 +0000 (UTC) To: comp.lang.ada@ada.eu.org Return-Path: X-Authentication-Warning: mail.eurocopter.com: uucp set sender to using -f Content-MD5: nPBjy9ciyi2MK9k6zFsm+g== X-Mailer: dtmail 1.2.1 CDE Version 1.2.1 SunOS 5.6 sun4u sparc X-BeenThere: comp.lang.ada@ada.eu.org X-Mailman-Version: 2.1 Precedence: list List-Id: comp.lang.ada mail to news gateway List-Unsubscribe: , List-Post: List-Help: List-Subscribe: , Xref: archiver1.google.com comp.lang.ada:33747 Date: 2003-02-04T10:13:59+01:00 > "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 I'm out of words with this statement... Why on earth do you think that each and every trait of a superset is going to hold in subsets? That's a very peculiar definiton of "subset", to say at least. > 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.