Re: GCD(0,0)

On Thu, 29 Dec 2005 20:58:08 -0500, quasi <quasi@xxxxxxxx> wrote:

>On 29 Dec 2005 19:59:26 -0500, hrubin@xxxxxxxxxxxxxxxxxxxx (Herman
>Rubin) wrote:
>
>>In article <1135888209.029280.145500@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
>>Leroy Quet <qqquet@xxxxxxxxxxxxxx> wrote:
>>>
>>>But what is, if there is any defined value,
>>>
>>>GCD(0,0)?
>>>
>>>Or is GCD(0,0) simply undefined, like 0/0?
>>
>>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.
>
>So you proclaim.
>
>Let's see what the books have to say.

Ok, I'll start it off with Sierpinski ...

Sierpinski, Elementary Theory of Numbers, 1964

Sierpinski defines GCD for any nonempty set S of integers (possibly
infinite) provided at least one element of S is nonzero.

quasi
.

Relevant Pages

  • Re: GCD(0,0)
    ... >>>When it comes to common divisors, ... >>>divides 0, and otherwise an integer never divides ... I'll start it off with Sierpinski ... ...
    (sci.math)
  • Re: GCD(0,0)
    ... >>>When it comes to common divisors, ... >>>divides 0, and otherwise an integer never divides ... >>my point of view the G in GCD says it all. ... The usual Euclidean Algorithm applied to 0 and 0 would require dividing ...
    (sci.math)
  • Re: simple GCD question (but has me foxed)
    ... That's an awkward proof. ... Any integer that divides two of these things ... So the set of _all_ common divisors x and y is the ... as the set of common divisors of x and x-y. ...
    (sci.math)
  • Re: simple GCD question (but has me foxed)
    ... the GCD, ... Any integer that divides both x and y must also divide x-y, ... that both /sets/ of common divisors are exactly the same. ...
    (sci.math)
  • Re: simple GCD question (but has me foxed)
    ... Any integer that divides both x and y must also divide x-y, ... following the "gcd is the largest common divisor" definition you ... that both /sets/ of common divisors are exactly the same. ... Don't really care at this point. ...
    (sci.math)
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