Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!umich!samsung!brutus.cs.uiuc.edu!psuvax1!psuvm!auvm!SUHEP!ANEZIRIS
From: ANEZIRIS@SUHEP.BITNET
Newsgroups: bit.listserv.hellas
Subject: Quiz
Message-ID: <HELLAS%90020917493569@BROWNVM.BITNET>
Date: 9 Feb 90 22:45:00 GMT
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Reply-To: The Hellenic Discussion  List <HELLAS@AUVM>
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    Oi migadikoi arithmoi ehoun apo dio tetragonikes rizes o kathenas, an y*y=x
tote (-y)*(-y)=x. Me tous pragmatikous dialegoume ti thetiki riza, me tous mi-
gadikous ta pragmata den einai toso apla. Otan grafeis 1=sqrt(-1)*sqrt(-1),
sqrt(-1) einai kai to i kai to -i, ara i ekfrasi den einai kai toso safis. To
mono pou simenei einai oti 1 anikei sto sinolo {i*i,i*(-i),(-i)*i,(-i)*(-i)}.
Afto ontos simvenei. Me trik tetragonikon rizon "apodiknieis" o,ti thes, p.h.
b*b=(-b)*(-b), ara a+b=a-b.

    Tora mia alli erotisi: orizoume to i na einai i tetragoniki riza tou -1. An
kaneis mas rotisei "poia apo tis dio" ti apantame;

    Telos: to polionimo ax**n + bx**(n-1) + ... + fx + g  opou a,b,...,g einai
n+1 pragmatikoi sintelestes, mporei na min ehei kamia pragmatiki riza, p.h.
x**2 + 1 . An oi sintelestes einai migadikoi, ehei panta migadiki riza; Nomizo
oti i apantisi einai katafatiki kai i apodiksi topologiki.

                                Xarilaos Aneziris