Re: [Haskell-cafe] Re: gcd

Am Sonntag 03 Mai 2009 18:16:38 schrieb Achim Schneider:

Nathan Bloomfield 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 :-(