Proof that 2 = 1

let a = b

a� = ab

Multiply both sides by a

a� + a� - 2ab = ab + a� - 2ab

Add (a� - 2ab) to both sides

2(a� - ab) = a� - ab

Factor the left, and collect like terms on the right

2 = 1

Divide both sides by (a� - ab)

This proof can also be used as a proof by contradiction that a can never be equal to b.

Index of joke proofs

An alternative proof that 2=1

A proof by induction that e = π

The webmaster and author of this Math Help site is Graeme McRae.

document.write (document.title)