On 6/07/2017 5:55 pm, Russell Standish wrote:
On Thu, Jul 06, 2017 at 04:18:49PM +1000, Bruce Kellett wrote:
On 6/07/2017 2:33 pm, Russell Standish wrote:
Establishing linearity is key.
Yes, and you haven't made progress with that.
All I ask is to give me some more time on this. I have some further
ideas in this regard, but need some dedicated time to think about it.
I have been thinking about it as well. I think your problem is even more
difficult that just establishing that the sum of two observer moments is
also an observer moment. If OMs are to form a linear vector space, they
have to satisfy some further axioms:
The axioms of associativity and commutativity are fairly easy if you
have additivity, but the existence of a zero vector, 0, such that V + 0
= V for any vector V in the space, and the existence of an inverse, -V,
s.t. V + (-V) = 0, might be more difficult in terms of OMs. What is a
null OM? What is an inverse (negative) OM?
I think you need these properties as well as additivity in order to have
a vector space. At least, these are among the axioms for a vector space
as listed by Wikipedia.
Bruce
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