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Erdős problem 1014

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Let R(k,l)R(k,l) be the Ramsey number, so the minimal nn such that every graph on at least nn vertices contains either a KkK_k or an independent set on ll vertices.

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FormalConjectures/ErdosProblems/

1014.lean

Retained formal statement1 of 2

Let R(k,l)R(k,l) be the Ramsey number, so the minimal nn such that every graph on at least nn vertices contains either a KkK_k or an independent set on ll vertices.

Prove, for fixed k≥3k\geq 3, that lim⁡l→∞R(k,l+1)R(k,l)=1.\lim_{l\to \infty}\frac{R(k,l+1)}{R(k,l)}=1.

This has been solved by an internal model at OpenAI.

FormalConjectures/ErdosProblems/1014.leanErdos1014.erdos_10141 lineExact file
∀ (k : ℕ), 3 ≤ k → Filter.Tendsto (fun l => ↑R(k, l + 1) / ↑R(k, l)) Filter.atTop (nhds 1)
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.