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From: ken@turtleva.UUCP (Ken Turkowski)
Newsgroups: net.math
Subject: Re: -1 = 1, and 1 = 2 "proofs"
Message-ID: <229@turtleva.UUCP>
Date: Tue, 20-Sep-83 00:53:36 EDT
Article-I.D.: turtleva.229
Posted: Tue Sep 20 00:53:36 1983
Date-Received: Wed, 14-Sep-83 04:18:48 EDT
References: cbscd5.551
Lines: 19

Regarding the proof that 2 = 1 via calculus,

	x^2 = x + x + ... + x (x times)
	2x  = 1 + 1 + ... + 1 (x times)
	2x = x
	2 = 1

What the author fails to see is that in the first expression,
x is really a parameter,

	x^2 = x * x

By the product rule for derivatives,

	d/dx { x * x } = 1 * x + x * 1 = 2 * x, not 1 * x

			Ken Turkowski
		    CADLINC, Palo Alto
		{decwrl,amd70}!turtlevax!ken