Talk:Examples of vector spaces

Unbounded sequences

in section "infinite coordinate space" there is a slight confusion about "unbounded sequences" which seem here to refer to infinite sequences while it usually means that the image of the sequence is unbounded (i.e. the set of all elements { x_i ; i\in\N } is unbound in F (whatever its topology may be), e.g. for C that (lim)sup|x_i|=∞). — MFH: Talk 19:27, 27 May 2005 (UTC)[reply]

Yes, unbounded is probably not the right word. I not sure what the proper language is for distinguishing between

a finite sequence
an infinite sequence with only finitely many nonzero terms
an infinite sequence with infinitely many nonzero terms.

I suppose one could gloss over the distinction between the first two items (which strictly speaking have different function domains) and call both finite sequences although that doesn't quite seem right to me. -- Fropuff 20:14, 2005 May 27 (UTC)

Fields

Why does this article talk so much about fields? the set of integers over the integers is a vector space, but not a field.. maybe this should be made clear (even though they aren't that common in usage) --yoshi 23:06, 11 January 2006 (UTC)[reply]

Fields are included in the definition of a vector space. Generalizations to commutative rings are called modules. The integers are indeed a Z-module, but that is not what this page is discussing. -- Fropuff 23:24, 11 January 2006 (UTC)[reply]