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 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: 2003-02-03 04:58:16 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!headwall.stanford.edu!fu-berlin.de!uni-berlin.de!tar-alcarin.cbb-automation.DE!not-for-mail From: Dmitry A. Kazakov Newsgroups: comp.lang.ada Subject: Re: Anybody in US using ADA ? One silly idea.. Date: Mon, 03 Feb 2003 13:58:10 +0100 Message-ID: References: <1043773909.385612@master.nyc.kbcfp.com> <1043855067.848326@master.nyc.kbcfp.com> <1043938878.313737@master.nyc.kbcfp.com> <1043949677.919365@master.nyc.kbcfp.com> <1044025904.464559@master.nyc.kbcfp.com> <6Hq%9.66948$F63.1363642@news.xtra.co.nz> NNTP-Posting-Host: tar-alcarin.cbb-automation.de (212.79.194.111) Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Trace: fu-berlin.de 1044277095 37246275 212.79.194.111 (16 [77047]) X-Newsreader: Forte Agent 1.8/32.548 Xref: archiver1.google.com comp.lang.ada:33719 Date: 2003-02-03T13:58:10+01:00 List-Id: On Mon, 3 Feb 2003 22:34:42 -0800, "AG" wrote: >"Dmitry A. Kazakov" wrote in message >news:qb6l3vglt4ur5svph1dn11o7dfmp8gl8c5@4ax.com... >> On Fri, 31 Jan 2003 10:11:44 -0500, Hyman Rosen >> wrote: >> >> >No, it is not, assuming the universe of allowed operations on >> >doubles. The compiler converts the int to a double, but the int >> >itself is not a double. >> >> 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. Exactly. There are two different statements: 1. The set of integers is a subset of the set of reals. 2. The set of the statements valid for the set of integers is a subset of the statements valid for the set of reals. 1. does not imply 2. Moreover, 2 is false. One could also put it otherwise: 1a. integer is a real 2a. integers is not reals => Integer is not a LSP-subtype of Float. N.B. Float is also not a LSP-subtype of real, and there cannot be such. However in most cases it is not an issue. Similarly, there might be contexts where Integer could be considered as a subtype of Float. --- Regards, Dmitry Kazakov www.dmitry-kazakov.de