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Is there a set A ⊆ R with the following property? In each case give an...

Is there a set A ⊆ R with the following property? In each case give an example, or a rigorous proof that it does not exist.

d) Every real number is both a lower and an upper bound for A.

(e) A is non-empty and 2inf(A) < a < 1 sup(A) for every a ∈ A.2

(f) A is non-empty and (inf(A),sup(A)) ⊆ [a+ 1,b− 1] for some a,b ∈ A and n > 1000.

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