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This (fabricated) draft student paper is designed to start a class discussion about when conceptual explanations are needed in mathematical writing. The paper is about an algorithm for finding square roots. The first proof shows that the algorithm is correct, but the point of the second proof is never clearly stated (it shows that the algorithm is efficient). Written by Joel Lewis for M.I.T.’s communication-intensive offering of Real Analysis, based on Rudin’s Exercise 16 in Chapter 3.

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