All open problems
Source labels openChecked July 26, 2026
Erdős Problem 44: Empty Start
The case where we start with an empty set (constructing large Sidon sets).
Mathematical statement
The case where we start with an empty set (constructing large Sidon sets).
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_44.variants.empty_start
Complete statement target, proof intentionally absentLean 4
theorem erdos_44.variants.empty_start : answer(sorry) ↔ ∀ᵉ (ε > (0 : ℝ)), ∀ᶠ (M : ℕ) in Filter.atTop, ∃ᵉ (A ⊆ Finset.Icc 1 M), IsSidon (A : Set ℕ) ∧ (1 - ε) * Real.sqrt M ≤ A.card := 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