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3. Assume √2 ∈R. Let S = { rational numbers q : q < √2 }....

3. Assume √2 ∈R. Let S = { rational numbers q : q < √2 }. (a)(i) Show that S is nonempty. (ii) Prove that S is bounded from above, but is not bounded from below. (b) Prove that supS = √2.

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