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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

675.0. "A proof that 2=1 !!" by APEHUB::ASFOUR () Fri Mar 13 1987 15:16

    Here's a proof that 2=1 that was presented to me during one of the
    math classes at High School. Although it contains a very basic mistake,
    I've managed to stump many engineers, and yes, some math majors!!
    To make things worse, the only person who figured it out was an
    Architect!! I hope DEC people do better!!
    
    
    Here it is  (I'll say why it's wrong sometime later)
    
    
    Let:          x=y
    
    Then:
		  x=y
             	x^2=x*y		       
    	    x^2-y^2=x*y-y^2		
    	(x-y)*(x+y)=y*(x-y)	
    	        x+y=y		
   	        y+y=y		
                 2y=y
 therefore        2=1

   
    
    					Enjoy. 
T.RTitleUserPersonal
Name
DateLines
675.1SolutionJON::MORONEYLight the fuse and RUN!Fri Mar 13 1987 15:5233

    Let:          x=y
    
    Then:
		  x=y
             	x^2=x*y		       
    	    x^2-y^2=x*y-y^2		
>    	(x-y)*(x+y)=y*(x-y)		If x=y, this line is 0 * something.
					Both sides are 0, since (x-y) = 0.
>    	        x+y=y			To get this, you have divided both sides
					by 0. (naughty naughty!)
   	        y+y=y		
                 2y=y
 therefore        2=1


Here's a similar one, proving 2<1

    Let:          0<x<y
    
    Then:
		  x<y
             	x^2<x*y		       
    	    x^2-y^2<x*y-y^2		
    	(x-y)*(x+y)<y*(x-y)
    	        x+y<y	
   	        y+y<y		
                 2y<y
 therefore        2<1

I used to do these all the time to a math teacher when I was a kid.

-Mike
675.2yes, devide by zero will let you show 1=2THEBUS::KOSTASWisdom is the child of experience.Fri Mar 13 1987 16:088
    re. -1
    
    well you may find a few of the problems in this notes file.
    
    In your example, division by zero is the problem.
    
    /kgg
    
675.3take a look at note 466.* for similar ideasTHEBUS::KOSTASWisdom is the child of experience.Fri Mar 13 1987 16:144
    re. .0
    
    take a look at some of the ideas in the note 466.*
    
675.4very old!IOSG::DEMORGANMon Jun 15 1987 10:121
    This was a hoary old chestnut thirty years ago.