fix(ErdosProblems/33) #1573
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fix(ErdosProblems/33) #1573
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YaelDillies
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Jan 17, 2026
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| theorem erdos_33 : IsLeast | ||
| { c : EReal | ∃ (A : Set ℕ), AdditiveBasisCondition A ∧ | ||
| Filter.atTop.limsup (fun N => (A.interIcc 1 N).ncard / √N) = c} | ||
| answer(sorry) := by | ||
| theorem erdos_33 : ⨅ A : {A : Set ℕ | AdditiveBasisCondition A}, Filter.atTop.limsup (fun N => | ||
| (A.1.interIcc 1 N).ncard / (√N : EReal)) = answer(sorry) := by |
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I'm not sure I understand this change. Can you explain?
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The infimum of a set s may not belong to that set, while IsLeast s ∈ s. Based on the problem description, I don't think we know that the infimum is attained by some element.
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Closes #1543
van Doorn's constructions implies that there exists a set
Asuch thatlim sup |A ∩ {1, …, N}| / N^(1/2) ≤ (2 * (φ ^ (5 / 2))). Hence, the minimum value oflimsupis less than(2 * (φ ^ (5 / 2))).Also fixes some typos.