Anonymous wrote: > George: > >>I was taught (33 years ago in the University of Birmingham, UK) that a >>vector space is >>(1) a set of elements (the vectors) which form an abelian group under >>addition; >>(2) etc.... >>The phrase "commutative group" or "additive group" might have been used >>instead of "abelian group"--you'll forgive me if I can't quite remember! >> > > I think you just made me remember what an abelian group is. > It's closed under its operation, it's associative, commutative, > it's got an inverse, and it's got the identity element in it. > There may be some other condition, since aren't > all the above needed for any group? > I remember something about an abelian group forming a table > with a diagonal, or something....
(1) too many "It's", referring to different things.
(2) this would be an excellent time, to grab a textbook or your notes and _lookup_ the definition of "group" and "abelian group".
> > So, basically, "abelian group" is just an easier way of > saying "vector space".
> Rather than listing all 8 conditions. But, that assumes the student *knows* > what an abelian group is.
Not really. One can list all the conditions; but it would be nice at least to group the conditions in a coherent way and to mention those conditions that correspond to the axioms for an abelian group. Those students who have met "abelian groups" before would benefit and the others would not be hurt.