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From: tightgas@nmtvax.UUCP
Newsgroups: net.math
Subject: Re: 1 = 2 'proof'
Message-ID: <440@nmtvax.UUCP>
Date: Mon, 12-Sep-83 04:03:19 EDT
Article-I.D.: nmtvax.440
Posted: Mon Sep 12 04:03:19 1983
Date-Received: Mon, 12-Sep-83 20:01:25 EDT
Organization: New Mexico Tech, Socorro, NM
Lines: 26

Larry Cipriani submitted a 2 = 1 'proof' that began with
x^2 =  x + x + ... + x	(x times).

The number of terms on the right-hand side is also a function of x.
Therefore, IF the right-hand side can be differentiated with respect
to x (however, see below **), it is subject to differentiation just as
though the equation were written as

x^2 = x*x

Thus,
2*x = 1*x + x*1
2*x = 2*x
2 = 2

----------

** Presumably, the number of times x is written on the right-hand
side is an integer.  Since this is x times, it appears that
x can only have integer values.
Therefore, x is not continuous.
I think that x has to be continuous in order to differentiate
with respect to x.

Neal Kilmer
New Mexico Tech