gcd 0 0 = 0

[Marc van Dongen]

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
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