How can I prove that 1 = 0?
Just For Fun
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There is a way to show that one equals zero, and it includes an interesting “proof”:
Consider two nonzero 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 nonzero, 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.