On 23.05.2012 19:43 Stephen P. King said the following:


There seems to be a divergence of definitions occurring. It might be
 better for me to withdraw from philosophical discussions for a while
and focus just on mathematical questions, like the dependence on
order of a basis...

I believe that to this end, one just needs to number basis vectors, so we must order them. If I remember correctly, depending on how you order x, y, z you obtain either a right or left-handed coordinate system.


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