## Recreational Math## Just For Fun |

## How can I prove that 1 = 0? |

There is a way to show that one equals zero, and it includes an interesting “proof”:

Consider two non-zero numbers x and y such that x = y. If that is so, then x^{2} = xy. Subtracting y^{2} from both sides gives: x^{2} - y^{2} = xy - y^{2}. Then dividing by (x - y) gives x + y = y; and since × = y, then 2y = y. Thus 2 = 1; the proof started with y as a non-zero, so subtracting 1 from both sides gives 1 = 0.

The problem with this proof? If x = y, then x - y = 0. Notice that halfway through the “proof,” the equation was divided by (x - y), which makes the proof erroneous.