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Mathematicians speak of the set R of real numbers which, of course, consists of positive and negative numbers. A scalar is a member of the set R (see, e.g., Birkhoff & McLean, <A Survey of Modern Algebra> (McMillan 1953)). The unfortunate influence of the French School, Bourbaki, encourages us to make all definitions set-theoretical.
Help me out here. We have something that is not a scalar. It has
magnitude *and direction*. But is not a vector. So, what is it?
Do mathematicians have a name for this type of non-scalar non-vector
quantity?