Carefully prove the following propositions. Proposition 1.The only sets in R with empty boundary are ∅ and R. Proposition 2.The set S of rational numbers in the interval(0,1)cannot be expressed as the

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Carefully prove the following propositions.

Proposition 1.The only sets in R with empty boundary are ∅ and R.

Proposition 2.The set S of rational numbers in the interval(0,1)cannot be expressed as the intersection of a countable collection of open sets.

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