Erdős Problem 330
Does there exist a minimal basis with positive density such that, for any , the (upper) density of integers which cannot be represented without using is positive?
Mathematical statement
Does there exist a minimal basis with positive density such that, for any , the (upper) density of integers which cannot be represented without using is positive?
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_330_statement
theorem erdos_330_statement : answer(sorry) ↔ ∃ (A : Set ℕ), ∃ h, MinAsymptoticAddBasisOfOrder A h ∧ A.HasPosDensity ∧ ∀ n ∈ A, Set.HasPosDensity (UnrepWithout A n h) := 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