A friend showed me this proof:
Proof: 2 = 1
$$Let \space x= y$$
Multiply both sides by x:
$$x^2= xy$$
Subtract $y^2$ from both sides:
$$x^2-y^2= xy-y^2$$
Factor:
$$(x+y)(x-y) = y(x-y)$$
Cancel out $(x-y)$ from both sides:
$$(x+y) = y$$
Simplify (Because $x=y$):
$$y+y=y$$
$$2y = y$$
$$2 = 1$$
Where does the logic break down? Everything is done to both sides.
$\endgroup$ 51 Answer
$\begingroup$You cannot cancel out the $(x-y)$. You defined $x=y$, so you end up dividing by $0$.
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