Is 2 = 1?

            x = y           (1) Assume x is equal y
          x*x = x*y         (2) Multiply both sides by x
    x*x - y*y = x*y - y*y   (3) Subtract y*y from both sides
  (x-y)*(x+y) = (x-y)*y     (4) Factor (x-y) from both sides
        (x+y) = y           (5) Cancel (x-y) from both sides
        (x+x) = x           (6) Since x=y from eq. (1), replace y with x
           2x = x           (7) Simplify
            2 = 1           (8) Cancel x from both sides

From the fact that we cannot divide any number by zero, we can conclude the following:

Since x is equal to y (from Eq. 1), canceling out x-y (which is equal to zero) to get to Equation 5 is not allowed. Remember, canceling out x-y is the same as dividing both sides of the equation by x-y, thereby performing a division by zero operation. Since an invalid operation is performed to get to Equation 5, all equations, including 2 = 1 (as we know), that are derived from Equation 5 are invalid.


  1. I’m lost, whats an x? 🙂

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