Riddle: One Equals Two
Consider the following explanation for why 1=2 :
1. Start out | Let y = x | |
2. Multiply through by x | xy = x^{2} | |
3. Subtract y^{2} from each side | xy - y^{2} = x^{2} - y^{2} | |
4. Factor each side | y(x-y) = (x+y)(x-y) | |
5. Divide both sides by (x-y) | y = x+y | |
6. Divide both sides by y | y/y = x/y + y/y | |
7. And so... | 1 = x/y + 1 | |
8. Since x=y, x/y = 1 | 1 = 1 + 1 | |
8. And so... | 1 = 2 |
How is this possible?
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