Journal Quantum Jim's Journal: My /. fortune is mistaken 4
My
(1) X=Y ; Given
(2) X^2=XY ; Multiply both sides by X
(3) X^2-Y^2=XY-Y^2 ; Subtract Y^2 from both sides
(4) (X+Y)(X-Y)=Y(X-Y) ; Factor
(5) X+Y=Y ; Cancel out (X-Y) term
(6) 2Y=Y ; Substitute X for Y, by equation 1
(7) 2=1 ; Divide both sides by Y
-- "Omni", proof that 2 equals 1
However, you can only cancel out the (X-Y) if X != Y because if they are equal then the expression is zero! Indeed, the rest of the steps can be left, so you end up with:
2(x-y) = (x-y)
0 = 0
Friends don't let friends divide by zero!
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