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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....
--
Peter Hunsberger
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