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Source labels openChecked July 26, 2026

Erdős ProblemsCombinatorics

Erdős Problem 949

Let S⊆RS \subseteq \mathbb{R} be a set containing no solutions to a+b=ca + b = c. Must there be a set A⊆R∖SA \subseteq \mathbb{R} \setminus S of cardinality continuum such that A+A⊆R∖SA + A \subseteq \mathbb{R}\setminus S?

CombinatoricsAMS 5

Mathematical statement

Let S⊆RS \subseteq \mathbb{R} be a set containing no solutions to a+b=ca + b = c. Must there be a set A⊆R∖SA \subseteq \mathbb{R} \setminus S of cardinality continuum such that A+A⊆R∖SA + A \subseteq \mathbb{R}\setminus S?

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_949

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_949 : answer(sorry) ↔    ∀ S : Set ℝ, (∀ a ∈ S, ∀ b ∈ S, a + b ∉ S) → ∃ A ⊆ Sᶜ, #A = 𝔠 ∧ A + A ⊆ Sᶜ := 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

Pinned Formal Conjectures sourceformalizationerdosproblems.com/949background