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3a) Prove that for any rational number and any irrational number there exists an irrational number between them. A proof by contradiction is a suggested

3a) Prove that for any rational number and any irrational number there exists an irrational

number between them. A proof by contradiction is a suggested approach

3b) Show that if n is an irrational number, there exists a unique integer where the distance between n and that integer is strictly less than 0.5.

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