Re: GCD(0,0)
- From: hrubin@xxxxxxxxxxxxxxxxxxxx (Herman Rubin)
- Date: 29 Dec 2005 19:59:26 -0500
In article <1135888209.029280.145500@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Leroy Quet <qqquet@xxxxxxxxxxxxxx> wrote:
>I notice that these math-controversy threads often get massive
>numbers of replies.
>(While more serious math posts and my games, for example,
>hardly ever get any replies.)
>So I will post this troll-bait flame-bait message to sci.math
>because I always wanted to start one of those huge threads.
>:)
>For n = any positive integer, it is known that
>GCD(n,n) = n
>and
>GCD(0,n) = n.
>(GCD is Greatest Common Divisor, of course.)
>But what is, if there is any defined value,
>GCD(0,0)?
>It certainly isn't 0 (which would fit the pattern above if
>n=0), is it?
>I would think that infinity would work as well as anything.
>Or is GCD(0,0) simply undefined, like 0/0?
>thanks, (half seriously, oh well, 3/4 seriously)
>Leroy Quet
When it comes to common divisors, since everything
divides 0, and otherwise an integer never divides
a smaller integer, for this purpose, 0 is the
greatest common divisor of 0 and 0. The ordering
is that of divisibility. This also holds for
least common multiple.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Department of Statistics, Purdue University
hrubin@xxxxxxxxxxxxxxx Phone: (765)494-6054 FAX: (765)494-0558
.
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