From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3224 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: fundamental theorem of algebra Date: Mon, 3 Apr 2006 21:08:03 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241019167 7774 80.91.229.2 (29 Apr 2009 15:32:47 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:32:47 +0000 (UTC) To: categories Original-X-From: rrosebru@mta.ca Tue Apr 4 02:27:50 2006 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 04 Apr 2006 02:27:50 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.52) id 1FQe14-0000Er-V2 for categories-list@mta.ca; Tue, 04 Apr 2006 02:23:47 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 21 Original-Lines: 32 Xref: news.gmane.org gmane.science.mathematics.categories:3224 Archived-At: Perhaps the moral is not to bother with the Britannica. Wikipedia has several proofs including the winding number argument and the one I outlined using the symmetric function argument. Then a couple of analytic ones. Of course, Wiki has no size limitations. Perhaps we have flogged this particular horse enough. On Sun, 2 Apr 2006, Vaughan Pratt wrote: > Fred E.J. Linton wrote: > > First, in Birkhoff & Mac Lane (my own undergraduate algebra text), > > Section 3 of Chapter V of the 1953 ("revised") edition offers a > > proof along winding number lines on pp. 107-109. > > Thanks, Fred, I wish I'd noticed that before. I have the sixth printing > (1948) of the 1941 edition, which says, "Many proofs...are known; ...we > have selected one whose non-algebraic part is *especially plausible > intuitively*." (My emphasis.) Then they give the proof "I like". > > To administer one more lash to this dead horse, the wording in the > Britannica article implies that the absence of an elementary algebraic > argument was the reason for omission of a proof of FTAlg. Whence the > change of heart about arguments that are "especially plausible > intuitively?" If they're good enough for an algebra text they should be > even more acceptable for an encyclopaedia article. > > Vaughan Pratt > >