[Haskell-cafe] Re: gcd

Daniel Fischer daniel.is.fischer at web.de
Sun May 3 14:56:25 EDT 2009

Am Sonntag 03 Mai 2009 18:16:38 schrieb Achim Schneider:
> Nathan Bloomfield <nbloomf at gmail.com> wrote:
> > The "greatest" in gcd is not w.r.t. the canonical ordering on the
> > naturals; rather w.r.t. the partial order given by the divides
> > relation.

Nitpick: it's not a partial order, but a preorder (2 | (-2), (-2) | 2, 2 /= (-2)).

> This, to defend myself, was not how it was explained in high school.

Understandably. One wouldn't want to confuse the average pupil with too abstract concepts 
like arbitrary rings or preorders. Unfortunately that leads to teaching concepts of 
primes, greatest common divisors and least common multiples which don't agree with the 
modern mathematical concepts :-(

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