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Proof That 2 Does Equal 1!

Date: 03/24/97 at 21:47:56
From: Anonymous
Subject: 2 Does Equal 1!

I was sitting in English Class, and, Math being my TRUE subject 
:), I got bored and started thinking of math.  I wrote out a little 
proof that 2 = 1.  I know that it's impossible, so I thought that you 
could show me where the proof goes wrong.  Here it is:

1)     x = y 
2)     x^2 = xy      (multiply both sides by x)
3)     x^2 - y^2 = xy - y^2  (subtract y^2 from each side)
4)     (x + y)(x - y) = y(x - y)     (factor)
5)     x + y = y     (divide out (x - y))
6)     2y = y      (substitute y for x from #1)
7)     2 = 1      (What do you think of that?!)

Thanks a lot Dr. Math!  You're a real inspiration to us resident 
Dr. Math Hopefuls!


Date: 03/25/97 at 14:38:02
From: Doctor Steven
Subject: Re: 2 Does Equal 1!

Your mistake comes in step 5, when you divided by (x-y) on both sides. 
Since x = y, x-y = 0, so you are dividing by zero, which is undefined 

Besides, if 2 = 1 then I'm the Pope. 

Proof:  2 = 1.  The Pope is one, and I'm one, so the Pope and I are 
two. From the equation, the Pope and I are one. So I am the Pope.  

-Doctor Steven and Dr. Chuck,  The Math Forum
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Associated Topics:
High School Number Theory

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