Talk:Linear Algebra/Definition of Vector Space

This page is in serious need of attention. I have gone through and tried to make at least some of the TeX code parse correctly. But I have run out of energy for this today. Here are some problems that still exist on this page. Thenub314 (talk) 12:15, 20 March 2009 (UTC)
 * 1) Lots of TeX code outside $$ $$ tags.
 * 2) When there are $$ $$ they get used incorrectly, often as parenthesis. Causing strange display problems.
 * 3) TeX style quotation marks are often used outide of math environments (that is `` and '' ) which lead to strange italics.
 * 4) There are some mathematical errors throughout.
 * 5) When specifying sets often there is simply a { instead of \{ so the braces don't appear. The arrow symbol is used as the set builder "such that" so for example the set of integers greater then five may be type set as $${a\in\mathbb{N}\to a>5}$$ instead of $$\{a\in\mathbb{N}\mid a>5\}$$ or $$\{a\in\mathbb{N} : a>5\}$$.
 * 6) Nonstandard tex commands are used so they fail to parse, as the cleanup tag currently points out. I have decided that \polyspace should just become a capital P.  There are also things like "\map{f}{N}{R}" for "f:N\to R" and "\nbym{2}{3}" for "2\times 3".
 * 7) There are a few places where the grammer is questionable.