Re: Is zero even or odd?
From: vonroach (hadrainc_at_earthlink.net)
Date: 12/22/04
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Date: Wed, 22 Dec 2004 14:43:11 GMT
On Tue, 21 Dec 2004 10:37:35 GMT, Fred Bloggs <nospam@nospam.com>
wrote:
>
>
>Kevin Aylward wrote:
>> Fred Bloggs wrote:
>>
>>>Alfred Z. Newmane wrote:
>>>
>>>>Nicholas O. Lindan wrote:
>>>>
>>>>
>>>>>"John Sefton" <john@petcom.com> wrote
>>>>>
>>>>>
>>>>>
>>>>>>0 can't be divided by itself,
>>>>>
>>>>>Sure it can: 0 / 0 = 0 * (1 / 0) = 0 * infinity = 1
>>>>>
>>>>>It works if the only three numbers in the universe are
>>>>>0, 1, and infinity -- A number system that seems very
>>>>>suited to usenet.
>>>>
>>>>
>>>>Except for the fact that: 0 / 0 = undefined
>>>>
>>>>Or actually more correct: n / 0 = undefined
>>>>
>>>>
>>>
>>>0/0={ SET OF ALL INTEGERS }
>>
>>
>> No.
>>
>>
>>>n/0= NULL SET for n<>0
>>>
>>>It is very well-defined.
>>
>>
>> No it isnt.
>>
>> Kevin Aylward
>
>You apparently have stumbled on something else you know damn little
>about. In case you need help with this , you might note that "/" is NOT
>an operator on the integers, it is the "inverse" of a multiplication
>operator. Inverse is a well-defined concept but not necessarily a
>function, it is a set theoretic mapping. E.G. m/n={ q: m=q*n} by
>definition, so that m/n which is actually a set which can be empty, a
>singleton, or infinite. In the case of m/n, it is then m/n = F^-1(m)
>where F(x)= n*x. Your reasoning would lead one to believe /: I x I -> I
>is a function, which it isn't.
Ah, the inverse , like 1/0 is inverse of 0/1? Is 0/0 the inverse of
0/0? And 1/1, the inverse of 1/1.
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