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Peter Hunsberger wrote:
>On Thu, 13 Jan 2005 09:03:56 +1100, Rick Marshall <rjm@zenucom.com> wrote:
>
>
>>Peter Hunsberger wrote:
>>
>>
>>
>>>On Thu, 13 Jan 2005 08:06:08 +1100, Rick Marshall <rjm@zenucom.com> wrote:
>>><snip/>
>>>
>>>
>
><snip/>
>
>
>
>>>Bad analogy Rick. In Group theory groups are, by definition, a set of
>>>elements (possibly infinite) that is closed over some operator.
>>>
>>>
>>>
>>i think that's what i said - although perhaps i was looking at an
>>interesting aspect of this closure - you can't tell if an instance of an
>>element of the set exists in it's own right or as the result of applying
>>the operator. ie you can't uniquely decompose an element of a group.
>>
>>
>>
>>><snip/>
>>>
>>>
>
>Umm, ok, but I think you're stretching :-) The whole point of a group
>is that it doesn't matter; there's no such thing as decomposition per
>se, just elements and an operator, that's why group isomorphism is
>such a powerful tool. (Closure just guarantees that if a . b is in
>the group then b . a is also in the group.)
>
>BTW, before people start to nitpick I realize that to completely
>define a group you also need associativity, an identity element and an
>inverse for every element....
>
>
>
yep, i agree. and yes i know all those things too.
decomposition fascinates me because we have 3000 years (at least) of
experience with it (back to the ancient greeks) and it pervades our
thinking.
rick
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