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From: Stephen Leake <stephen.a.leake.1@gsfc.nasa.gov>
Newsgroups: comp.lang.ada
Subject: Re: Dimensionality Checking (Ada 20XX)
Date: 12 Dec 2001 09:26:02 -0500
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dmitry@elros.cbb-automation.de (Dmitry A. Kazakov) writes:

> On 11 Dec 2001 11:39:30 -0500, Stephen Leake
> <stephen.a.leake.1@gsfc.nasa.gov> 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.

Hmm. Good point. I guess infinite series are trickier than I remember;
it has been a long time :).

-- 
-- Stephe