How can I prove that 1 = 0?

Just For Fun Read more from
Chapter Recreational Math

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 x2 = xy. Subtracting y2 from both sides gives: x2 - y2 = xy - y2. 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.


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