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Exercise1.2.1: Prove that if t > 0 (t∈R), then there exists an n∈N such that 1/n^2...

Exercise1.2.1: Prove that if t > 0 (t∈R), then there exists an n∈N such that 1/n^2 < t.

Exercise1.2.2: Prove that if t ≥ 0(t∈R), then there exists an n∈N such that n−1≤ t < n.

Exercise1.2.8: Show that for any two real numbers x and y such that x < y, there exists an irrational number s such that x < s < y. Hint: Apply the density of Q to x/(√2) and y/(√2).

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