# gcd 0 0 = 0

**Marc van Dongen
**
dongen@cs.ucc.ie

*Tue, 18 Dec 2001 09:22:25 +0000*

Ch. A. Herrmann (herrmann@infosun.fmi.uni-passau.de) wrote:
:* In contrast, 0*x=0, thus 0 "divides" 0 (somehow).
*:* But I have problems with "gcd being the greatest positive integer ..."
*
[snip]
:* - 0 is not positive, it is non-negative or natural
*:* - 2 also divides 0 and 2 is a "greater integer" than 0
*:* (0 is the top element of the lattice formed by the division relation
*:* but that is not clear by the expression "greatest")
*:*
*
gcd a b is the greatest non-negative integer dividing both a
and b such that anything that divides both a and b also divides
gcd a b (so gcd a b is the greatest thing that divides both a
and b).
Regards,
Marc van Dongen
--
Marc van Dongen | dongen@cs.ucc.ie |
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