I can prove why 1 = 2

* Lets say y = x

* Multiply through by x xy = x2

* Subtract y2 from each side xy - y2 = x2 - y2

* Factor each side y(x-y) = (x+y)(x-y)

* Divide both sides by (x-y) y = x+y

* Divide both sides by y y/y = x/y + y/y

* And so... 1 = x/y + 1

* Since x=y, x/y = 1 1 = 1 + 1

* And so... 1 = 2

How is this possible ?

Step 5 is invalid, because we are dividing by (x-y), and since x=y, we are thus dividing by 0. This is an invalid mathematical operation (division by 0), and so by not following basic mathematical rules