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From: leimkuhl@uiuccsb.UUCP
Newsgroups: net.math
Subject: Re: -1 = 1, and 1 = 2 'proofs' - (nf)
Message-ID: <2790@uiucdcs.UUCP>
Date: Sun, 11-Sep-83 22:33:25 EDT
Article-I.D.: uiucdcs.2790
Posted: Sun Sep 11 22:33:25 1983
Date-Received: Wed, 14-Sep-83 21:53:05 EDT
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#R:cbscd5:-55100:uiuccsb:9700005:000:613
uiuccsb!leimkuhl    Sep 11 19:27:00 1983


The proof that -1=1 is interesting since it points up the fact that the sqrt
function for positive reals is NOT like the complex square root.  In 
general, sqrt(x/y)=-sqrt(x)/sqrt(y) if x/y<0, x,y real.  One should use caution 
when applying results derived  in first year algebra courses before being  
acquainted with the complex domain.

In this case,	(1**(1/2))/((-1)**(1/2)) = 1/i = -i,
     while	(1/(-1))**(1/2) =(-1)**(1/2) = i

    so the statement sqrt(1/-1)=sqrt(1)/sqrt(-1) is false.

The second "paradox" is really dumb.  First you assume x is an integer, then
try to use real calculus.  Brilliant.