NetNews Usenet Archive 1992 #31/NN_1992_31.iso/spool/comp/lang/cplus/18501

Internet Message Format | 1992-12-29 | 1.9 KB

Xref: sparky comp.lang.c++:18501 sci.math:17483
Newsgroups: comp.lang.c++,sci.math
Path: sparky!uunet!zaphod.mps.ohio-state.edu!menudo.uh.edu!sugar!claird
From: [e-mail] (Cameron Laird)
Subject: Re: IS C++ a language for the "average programmer"
Organization: NeoSoft Communications Services -- [phone]
Date: Tue, 29 Dec 1992 16:27:19 GMT
Message-ID: <[e-mail]>
References: <[e-mail]> <[e-mail]> <[e-mail]>
Lines: 35

In article <[e-mail]> [e-mail] (John MAX Skaller) writes:
>In article <[e-mail]> [e-mail] (Tim Poston) writes:
>>Anybody who thinks they can prove that every complex polynomial
>>has at least one root without using analysis
>>(the study of the kind of proofs that apply to calculus),
>>see me after class.
>>
>
>    But this is silly, since R is constructed by analysis.
>Given R, and the fact that every positive real has a root in R,
Does "every positive real has a root in R"
give us something that "every polyn of odd
degree over R has a zero in R" does not?  I
have to strain to make sense of the first
of these quoted propositions.
>and every polyn of odd degree over R has a zero in R,
>the Fundamental Theorem of *Algebra* (all polyns over C can be reduced
>to linear factors) follows by algebra.
            .
            .
            .
Please, tell us more.  My best understanding
is that it's considerably more subtle than
you appear to be claiming.  In fact, do you
have a proof
1.  of the reducibility of quadratics
    over the complexes, which
2.  is free of analysis other than the
    solvability of odd-degree polynomials?
The ones I know are rather delicate.
--

Cameron Laird
[e-mail] ([e-mail])    [phone]
[e-mail] ([e-mail])      [phone]