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When asked to prove that the difference of any irrational

Question: a. When asked to prove that the difference of any irrational number and any rational number is irrational, a student began, "Suppose not. That is, suppose the difference of any irrational number and any rational number is rational." What is wrong with beginning the proof in this way?

b. Prove that the difference of any irrational number and any rational number is irrational.

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Mathematics: When asked to prove that the difference of any irrational

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