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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

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

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_158 : answer(sorry)   A : Set , A.Infinite  B2 2 A     liminf (fun N :  => (A ∩ .Iio N).ncard * (N : ) ^ (- 1 / 2 : )) 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