overstated / january 2008

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.