On 4/12/2013 12:34 AM, Wayne Throop wrote: > : fom <fomJUNK@nyms.net> > : And, it makes sense that it would be related through the functions > : because what is involved with polynomials, extension fields, and the > : fundamental theorem of algebra. > > The fundamental theorem of algebra: neither a fundamental of algebra, > nor a theorem of algebra. Discuss. >
Well, have I invited another argument over what people who earn a great deal more money than I ever will cannot seem to agree upon because "God told 'em so" and they would rather argue than anything else?
My usage comes from the presentation in Hungerford.
The reference refers to the field of complex numbers being algebraically closed. It has the corollary that every proper algebraic extension field of the real numbers is isomorphic to the field of the complex numbers.
I have no doubt that there are other published sources that refer to some other theorem by the phrase I used or deny the legitimacy of the theorem because it depends on real analysis for its proof.