All open problems
Source labels openChecked July 26, 2026
Erdős Problem 158
Let A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0?
Mathematical statement
Let A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0?
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_158
Complete statement target, proof intentionally absentLean 4
theorem erdos_158 : answer(sorry) ↔ ∀ A : Set ℕ, A.Infinite → B2 2 A → liminf (fun N : ℕ => (A ∩ .Iio N).ncard * (N : ℝ) ^ (- 1 / 2 : ℝ)) atTop = 0 := 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