Talk:Examples of vector spaces: Difference between revisions

Revision as of 23:06, 11 January 2006

Revision as of 23:24, 11 January 2006

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==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|=&infin;). [[User:MFH|<nowiki></nowiki>]]&mdash; [[User:MFH|MFH]]: [[User talk:MFH|Talk]] 19:27, 27 May 2005 (UTC)

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#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. -- [[User:Fropuff|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)

--[[User:Sciyoshi|yoshi]] 23:06, 11 January 2006 (UTC)

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