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Fallacious proof/All numbers are equal

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It does not follow in general from x^2 = y^2 that x = y. Instead, we have either that x = y or x = -y. In the given situation, we have that a - \frac{t}{2} = \frac{a - b}{2} = -\left(\frac{b - a}{2}\right) = - \left(b - \frac{t}{2}\right), and so this was the fallacious step.

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