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Irrational Numbers (a) Prove that for every rational number µ > 0, there exists an irrational...

Irrational Numbers

(a) Prove that for every rational number µ > 0, there exists an irrational number λ > 0 satisfying λ < µ.

(b) Prove that between every two distinct rational numbers there is at least one irrational number. (Hint: You may find (a) useful)

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