Proof that 2=1
x
=
y
x^2
=
xy
(multiply both sides by x)
x^2 - y^2
=
xy - y^2
(subtract y^2 from both sides)
(x + y)(x - y)
=
y(x - y)
(factored)
x + y
=
y
(divide both sides by (x - y))
y + y
=
y
(equation 1. says x = y)
2y
=
y
2
=
1
Why is this?