Erdős Problem 1199
Is it true that in any 2-colouring of there exists an infinite set such that all elements of are the same colour?
Mathematical statement
Is it true that in any 2-colouring of there exists an infinite set such that all elements of are the same colour?
A conjecture of Owings [Ow74].
Statement source: Erdős Problems statement material
Statement terms: Source-specific
Source-specific terms. Therefore does not assert reuse rights beyond attributed display.
Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
erdos_1199
theorem erdos_1199 : answer(sorry) ↔ ∀ (color : ℕ → Fin 2), ∃ (A : Set ℕ), A.Infinite ∧ ∀ n ∈ (A+A), ∀ m ∈ (A+A), color n = color m := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References