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From: lvc@cbscd5.UUCP
Newsgroups: net.math
Subject: Why -1 =/= 1
Message-ID: <569@cbscd5.UUCP>
Date: Wed, 14-Sep-83 10:46:15 EDT
Article-I.D.: cbscd5.569
Posted: Wed Sep 14 10:46:15 1983
Date-Received: Thu, 15-Sep-83 06:46:28 EDT
Organization: Bell Labs <SCCS>, Columbus
Lines: 26

The error in my 'proof' of -1 = 1 has to do with a wierd property of 
complex numbers.  

Here is the 'proof' again.

		-1 = -1  =>
		-1/1 = 1/-1  =>
		sqrt(-1/1) = sqrt(1/-1)  => (?)
		sqrt(-1)/sqrt(1) = sqrt(1)/sqrt(-1) =>
		sqrt(-1)*sqrt(-1) = sqrt(1)*sqrt(1)  =>
		-1 = 1

The problem is that sqrt(1/-1) =/= sqrt(1)/sqrt(-1).
sqrt(1/-1) is i, and sqrt(1)/sqrt(-1) is -i.  1/i = -i, not i.
The first time I saw this in 10th grade I was pretty shocked.

It seems that a lot of computer science people are getting hung up over
the fact that I said sqrt().  There is no other convenient way to express
the mathematicians function of square root (whose domain extends to all
real numbers, and complex as well) on a terminal.  Sorry for the
confusion.

Anyone figure out the error in the calculus 'proof' that 2 = 1 yet ?

Larry Cipriani
cbosgd!cbscd5!lvc