Proof that 2 = 1

From Overcoming Bias, a proof that 2 is, in fact, equal to one. First let x = y = 1.

  1. x = y
  2. x2 = xy
  3. x2 – y2 = xy – y2
  4. (x + y)(x – y) = y(x – y)
  5. x + y = y
  6. 2 = 1

There is a simple flaw in this proof that an astute observer will identify, but it’s still good for cocktail parties and stumping children on the border of abstract reasoning! Wikipedia has a page on invalid proofs for 1 = -1, 2 = 1, -2 = 1 and &infinity; = 1/4, all of which seem mighty plausible.