Dennis den Brok <d.den.brok%uni-bonn.de@localhost> writes:
> Aleksej Saushev <asau%inbox.ru@localhost> schrieb:
>> I know at least one school that doesn't teach mathematical analysis
>> using Cauchy-style definitions prefering to start from topology,
>> I know another (quite large!) school that introduces filters as soon as
>> possible to avoid dealing with handful of special cases, I was taught
>> Robinson (non-Archimedean) analysis in parallel to classical one.
>
> AFAIK, this is also referred to as "non-standard analysis"...
This was "non-standard" half a century ago or even more. When I was taught,
it wasn't considered non-standard, not even by those who taught classical
analysis. That may be specific to the university, but in two distant
universities when I asked questions about it, I was told rather mild
opinions between "well, pedagogical side is too controversial to my mind,
it involves such and such, and we don't teach it that early" to "that would
be nice to try even in general course, if pedagogical side were more
elaborate."
> Shouldn't NetBSD rather adhere to standards?
If you remember, NetBSD doesn't adhere to standards completely and,
what is more important, blindly.
Note that the first standard appeared later than those mathematical fields,
like constructive analysis or non-Archemedean analysis, considered by
"traditionalists" alien.
>> And as far as I remember there do exist schools that consider 1 as prime
>> number. Note that I didn't proclaim this ex cathedra and performed some
>> analysis of this possibility, while you didn't dare to bring anything to
>> support your point of view.
>
> There doesn't seem to be a good reason relevant to the purpose of
> a small tool included in an operating system, apart from that,
> indeed, most people do not consider 1 prime, because that is what
> they were taught at school and in most courses at university, or
> it is most convenient in their particular field of mathematical
> research.
>
> The manpage included in NetBSD less-or-equial 5.x does not even
> mention the word "prime", by the way, and so far negative integers
> have, contrary to what the manpage says, been rejected, so I suggest
> the wording to be changed such that "factor" is supposed to return
> a minimal factorization of a non-negative integer by numbers not
> further non-trivially decomposable.
> In particular, "factor x" yields "x: x" for x \in \{0,1\}.
>
> If absolutely required, I would let the manpage state that for
> negative integers their absolute values are factored as for
> non-negatives and then "x: -1 ${factors_of_|x|}" is returned.
>
> Maybe this can be agreed upon?
This is consequence (logically) of what I propose.
Mathematically, it is consistent with expectations of those whose
knowledge doesn't extend beyound "traditional" school. More, it is
consistent with traditional behaviour, when the number before colon
is product of the those after. That it handles negative inputs is
the "feature" like square root of negative number to those who lived
in 16th century (or whenever imaginary numbers were first imagined).
Technically, it is trivial to implement, and it is simpler, since it
spares from handling special cases as insisted by "traditionalists."
--
HE CE3OH...
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