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Erdős problem 268

Let X be the set of points in Fin d → ℝ of the shape fun i : Fin d => ∑' n : A, (1 : ℝ) / (n + i) for some infinite subset A ⊆ ℕ such that 1 / n is summable over A. X has nonempty interior. This is proved in [KoTa24]. -

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FormalConjectures/ErdosProblems/

268.lean

Retained formal statement1 of 1

Let X be the set of points in Fin d → ℝ of the shape fun i : Fin d => ∑' n : A, (1 : ℝ) / (n + i) for some infinite subset A ⊆ ℕ such that 1 / n is summable over A. X has nonempty interior. This is proved in [KoTa24]. -

FormalConjectures/ErdosProblems/268.leanErdos268.erdos_2682 linesExact file
∀ (d : ℕ),  (interior {x | ∃ A, A.Infinite ∧ (Summable fun n => 1 / ↑↑n) ∧ x = fun i => ∑' (n : ↑A), 1 / (↑↑n + ↑↑i)}).Nonempty
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

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