Re: GCD(0,0)


quasi wrote:

<snip>

>
> This thread started with the OP asking for the value, if any, of
> gcd(0,0). What surprised me was that so many people immediately jumped
> in and asserted gcd(0,0)=0,

In my case, I made no such assertion. I merely pointed out that
in two different programming environments, gcd(0,0) returns 0.

> leaving the clear impression that was the standard definition.

And it may very well be, where software is concerned, since as
David Ullrich pointed out, it is a consequence of the Euclidean
Algorithm.

> I felt obligated to challenge that since I was
> pretty sure it was not the standard.

And it may very well be that what is standard in programming
differs from what is standard in text books. In which case,
the student and researcher should at least be aware of the
discrepency.

>
> I gave some references -- Sierpinski, Hardy, Gilmer, Lang, and I'm
> sure you would agree that those authors are all highly reputable.
>
> To the extent that I took sides, it was from the point of view of
> elementary number theory. In that context, both definitions are
> acceptable, and both are equally useful, but I felt barring gcd(0,0)
> makes the concepts of gcd clearer for the beginning student.

As long as they don't get their hands on Excel or Python. Your goal,
although admirable, is a lost cause.

>
> But I think there are issues here that go beyond just gcd(0,0).
>
> Especially now that we have wikipedia and MathWorld (where I've seen
> some horrible definitions), both being viewed as "official" sources,
> the question as to what's the right choice for a standard definition
> will increasingly be a subject of heated debate.
>
> quasi
>
>
>
>
>
>
> if that was the standard.

.

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