This one isn't from the book It is a simple proof Here is a proof of something interesting It's a nice little example of various algebraic manipulations and an importan example of why we worry about the validity of expressions Start with two non zero numbers, x, and y, such that x y x xy Setting up two equivalent expressions x y xy y Subtract y from each side ximy xyry Divide through by (x y) x y x y SD, 2) Factor numerators xy x y x y y Cancel out (x y) yty ay Substitute y for x 2y y Combine like terms 2 Divide through by y 1 0 Subtract 1 from both sides So is the universe all wrong and one really is equal to zero If so, how were we so wrong for so long Or is there something wrong with the proof If the proof is the problem here then exactly what is the

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This one isn't from the book  It is a simple proof  Here is a proof of something interesting  It's a nice little example of various algebraic manipulations and an importan example of why we worry about the validity of expressions  Start with two non zero numbers, x, and y, such that x   y  x   xy Setting up two equivalent expressions x y xy y Subtract y   from each side ximy   xyry  Divide through by (x y) x y x y SD,   2) Factor numerators xy x y x y y Cancel out (x y) yty ay Substitute y for x 2y y Combine like terms 2   Divide through by y 1 0 Subtract 1 from both sides So    is the universe all wrong and one really is equal to zero  If so, how were we so wrong for so long  Or is there something wrong with the proof  If the proof is the problem here    then exactly what is the

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Question: This one isn't from the book. It is a simple proof. Here is a proof of something interesting. It's a nice little example of various

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