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=-0.3 required=5.0 tests=BAYES_00,FREEMAIL_FROM, REPLYTO_WITHOUT_TO_CC autolearn=no autolearn_force=no version=3.4.4 X-Google-Language: ENGLISH,ASCII-7-bit X-Google-Thread: 103376,86d333341f490421 X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2002-03-27 20:00:14 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!canoe.uoregon.edu!elk.ncren.net!nntp.upenn.edu!msunews!not-for-mail From: "Chad R. Meiners" Newsgroups: comp.lang.ada Subject: Re: Natural data type ? Date: Wed, 27 Mar 2002 22:55:14 -0500 Organization: Michigan State University Message-ID: References: <3CA12AD4.2030807@oek.dk> <3CA25342.1080906@oek.dk> Reply-To: "Chad R. Meiners" NNTP-Posting-Host: arctic.cse.msu.edu X-Priority: 3 X-MSMail-Priority: Normal X-Newsreader: Microsoft Outlook Express 6.00.2600.0000 X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2600.0000 Xref: archiver1.google.com comp.lang.ada:21743 Date: 2002-03-27T22:55:14-05:00 List-Id: I seriously doubt that someone made a random decision. There are many reasons to define N to include zero, for instance, the positive integers can easily represented as Z^+ while the negative integers may be represented as Z^-. There is a very nice symmetry with these representations of disjoint sets. It doesn't make sense to define the natural numbers to simply be the set of positive integer because you then have two competing names for the same set. Thus, it is better for the natural numbers (N) to be a different set from the positive integers (Z^+). Since zero isn't positive, this leaves N as the only candidate for containing zero. Very likely, whoever made this decision for Ada's data type of natural and positive had a similar rational reason for making this choice. I just don't see the designers flipping a coin or playing paper, scissors, rock to determine which data type gets zero ;) I wasn't around during Ada's initial design process; perhaps someone on comp.lang.ada was, and they know why or who made this decision or even if the decision was contested. -CRM "Peter I. Hansen" wrote in message news:3CA25342.1080906@oek.dk... > Chad R. Meiners wrote: > > >No misprint. The natural numbers can be define as containing zero as well > >as not containing zero. I know a good deal of mathematicians that define N > >to include zero; I also know a good deal of mathematicians that prefer N to > >only include positive whole numbers (zero is neither positive nor negative). > > > >-CRM > > > So, your answer is that someone just made a random decision ? > > /Peter >