Exercises relate to the following definition: Let (X, d) be a metric space. A subset D of X is said to be dense in X if cl D=X.
Prove that ℚ is dense in ℝ with the usual absolute value metric. [If a metric space (X, d) has a countable subset that is dense, then X is said to be separable. Thus in this exercise you are to show that ℝ is separable.]
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