Prove that 1 equals 0

  • Sometimes proofs aren't always as they seem. Look at the following proof that seems to follow sound mathematical logic. As you follow along try to see where the flaw in the logic is.

    x = y.
    Then x2 = xy.
    Subtract the same thing from both sides:
    x2 - y2 = xy - y2.
    Dividing by (x-y), obtain
    x + y = y.
    Since x = y, we see that
    2 y = y.
    Thus 2 = 1, since we started with y nonzero.
    Subtracting 1 from both sides,
    1 = 0.

    What's wrong with this "proof"?