1=0?

Date: Tue, 8 Nov 1994 09:22:00 -0500 (EST)
From: Salem HS
Subject: 1 = 0?

Don't know if this qualifies as a 'really good question,' but a group of 
students in an eighth grade math class here want to know how to prove 
that one actually equals zero.  Is it something like using the quadratic 
formula?

Thanks,

Cheri Harrison for Marcus Ellison

Salem Junior High School           e-mail: salem_jhs@solinet.net    
Library Media Specialists                  
Lithonia, GA  30038

From: Dr. Ethan
Date: Tue, 8 Nov 1994 10:47:50 -0500 (EST)

Well the first thing to say is that this cannot be done.  You cannot use
CORRECT mathematics to prove something that is untrue.  Secondly, 
yes I have constructed a proof.  My challenge to you is to find the 
obvious.  (I have seen more sophisticated proofs where the flaw is 
harder to find, but each one essentially has the same flaw that mine has)

        Given a = b  then this implies

        a - b + b = b   Now divide both sides by (a-b) and we have

        a - b + b  =   b
        _________    _____
          (a-b)      (a-b)

Then reduce the left side to be
              
        1 +      b     =     b
               _____       _____
               (a-b)       (a-b) 

Then subtract b/(a-b) from both sides and you have

                1=0      Wow, pretty neat huh.

Remember.  This is a flawed proof and no correct proof exists.  Untrue
things cannot be proved through correct mathematics.

        Ethan Doctor On Call