Re: [Phys-l] Types of scalars

[John Denker <jsd@av8n.com>]

On 01/02/2011 04:10 PM, David Bowman wrote:

> The example sum is not a vector in a two dimensional vector space if
> ordinary arithmetic is used along with the restriction that the apple
> number and orange number each be nonnegative integers.

Touché ... it's not actually a vector space.

In this context the term _semi-vector space_ has been used,
since /some/ of the vector-space axioms survive.

   Authors: Josef Janyška, Marco Modugno, Raffaele Vitolo
   Title: Semi-vector spaces and units of measurement
   http://arxiv.org/abs/arXiv:0710.1313

And perhaps more importantly, most of your intuitive notions
about vector spaces -- including dimensionality, adding vectors
tip-to-tail, etc. -- survive just fine.