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Peter Hunsberger wrote:
>On Thu, 13 Jan 2005 08:06:08 +1100, Rick Marshall <rjm@zenucom.com> wrote:
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>>and one final point - back to the sum is greater than the whole. i was
>>thinking about this in terms of an element algebra. group theory defines
>>a group by operations (verbs :) ) that when applied to members of the
>>group (usually, but i guess not necessarily, 2 members - could be
>>ternary operators) result in a member of the group. integer + integer =>
>>integer. but if you have a group member you have no way of knowing if it
>>was derived by operation (and there may be an infinite number of
>>contruction operations), which one, or does it just exist in it's own
>>right. the number 4 as an integer has different properties to the
>>numbers 1 and 3, but can be constructed from them.
>>
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>Bad analogy Rick. In Group theory groups are, by definition, a set of
>elements (possibly infinite) that is closed over some operator.
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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.
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