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

- x = y
- x
^{2} = xy
- x
^{2} – y^{2} = xy – y^{2}
- (x + y)(x – y) = y(x – y)
- x + y = y
- 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.

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(x-y)=0

You can’t divide with 0