FormalConjectures.ErdosProblems.«268»

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import FormalConjecturesUtil

Erdős Problem 268

Reference:

erdosproblems.com/268

[KoTa24] Kova\vC, V. and Tao T., On several irrationality problems for Ahmes series.


namespace Erdos268

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].

@[category research solved, AMS 40 54, formal_proof using lean4 at
  "https://gist.githubusercontent.com/madeve-unipi/62a8f68cdb4864b85b81a6752dcb0aa4/raw/5793aaa51089c25c37d8d63f60540367f6abe506/Erdos268.lean"]
theorem declaration uses 'sorry'erdos_268 (d : ℕ) : (interior {x : Fin d → ℝ | ∃ A : Set ℕ, A.Infinite ∧
    Summable (fun n : A => (1 : ℝ) / n ) ∧
    x = fun i : Fin d => ∑' n : A, (1 : ℝ) / (n + i)}).Nonempty := byd:ℕ⊢ (interior {x | ∃ A, A.Infinite ∧ (Summable fun n => 1 / ↑↑n) ∧ x = fun i => ∑' (n : ↑A), 1 / (↑↑n + ↑↑i)}).Nonempty
  sorryAll goals completed! 🐙


end Erdos268

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].

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].