Talk:Fundamental Theorem of Algebra

just started the article

This is some material that used to be in the complex number article, but I felt an entire article on the fundamental theorem of algebra would be the better place for it. However all I did was cut and paste from there to here, so this article doesn't have a good structure yet. Feel free to attack it! - Greg Martin 18:54, 29 April 2007 (CDT); clarified by Jitse Niesen 02:35, 9 May 2007 (CDT)

W.l.o.g.

What does this mean?--Paul Wormer 21:12, 13 March 2008 (CDT)

Also "counting multiplicity" - I'm guessing that it means that Tp=Tq (e.g. in (x + 2)(x + 2)), but you ought to say that explicitly. Other than that, great intro - crystal clear. J. Noel Chiappa 09:59, 14 March 2008 (CDT)

I think W.l.o.g. means "without loss of generality" and I don't see any connection with multiplicity of roots. You and I differing on intepretation, I wouldn't call the article crystal clear.--Paul Wormer 10:42, 14 March 2008 (CDT)

Umm, I just meant the intro was crystal clear. And my mention of "counting multiplicity" was in the sense of "what does this mean" - i.e. the article needs to be changed to make it clear. J. Noel Chiappa 13:53, 14 March 2008 (CDT)

Wlog is indeed "without loss of generality". I think it's bad style to use this abbreviation (even though people that know about homotopy groups probably know this abbreviation) so I wrote it out.

"Counting multiplicity" means what is says in the formula above that phrase. For instance, the quadratic polynomial $x^{2}-2x+1$ is only zero at $x=1$, but this is a double root because $x^{2}-2x+1=(x-1)^{2}$. So this root counts for two if we count roots with their multiplicities. -- Jitse Niesen 11:26, 15 March 2008 (CDT)