Question: 3.16. Let H C R be a nonempty set that contains the difference of every pair of its (not necessarily distinct) elements. Prove that either

3.16. Let H C R be a nonempty set that contains the difference of every pair of its (not necessarily distinct) elements. Prove that either there is a real number a such that H = {n . a : n E Z}, or H is everywhere dense. (* H)

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