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,cc4f25d878383cc X-Google-Attributes: gid103376,public X-Google-ArrivalTime: 2001-12-12 01:35:49 PST Path: archiver1.google.com!news1.google.com!newsfeed.stanford.edu!news-spur1.maxwell.syr.edu!news.maxwell.syr.edu!fu-berlin.de!uni-berlin.de!tar-alcarin.cbb-automation.DE!not-for-mail From: dmitry@elros.cbb-automation.de (Dmitry A. Kazakov) Newsgroups: comp.lang.ada Subject: Re: Dimensionality Checking (Ada 20XX) Date: Wed, 12 Dec 2001 09:35:47 GMT Message-ID: <3c17210a.3970375@News.CIS.DFN.DE> References: <11bf7180.0112070815.2625851b@posting.google.com> <9v0crt$bo2bi$1@ID-25716.news.dfncis.de> <9v37rs$cdmva$1@ID-25716.news.dfncis.de> NNTP-Posting-Host: tar-alcarin.cbb-automation.de (212.79.194.111) X-Trace: fu-berlin.de 1008149747 12780031 212.79.194.111 (16 [77047]) X-Newsreader: Forte Free Agent 1.21/32.243 Xref: archiver1.google.com comp.lang.ada:17822 Date: 2001-12-12T09:35:47+00:00 List-Id: On 11 Dec 2001 11:39:30 -0500, Stephen Leake wrote: >It is simply wrong to try to define units for trig and exponential >functions. Remember the Taylor expansion for Sin: > >Sin (x) = x - 1/6 x**3 ... > >If x has dimensions of meters (shudder :), then what are the >dimensions of Sin (x)? This is why angles must be dimensionless, as >radians are. It is true, but the proof is wrong. Consider sqrt (x). It also has a Taylor expansion in 1, which is also endless, yet sqrt (m**2) exists and is m. We just cannot use Taylor expansions before we define which dimension 2+2m could have. Not that it is impossible. Maybe there is a continiuation of the unit system where sqrt (m) or even exp (m) are defined. Who knows. But definitely, in SI only undimensioned values are allowed for all "non-trivial" functions. Regards, Dmitry Kazakov