Back to Problems

erdos_268

Specification

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].

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement
theorem 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
ID: ErdosProblems__268__erdos_268
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.