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Erdős problem 105

Let A,B⊂R2A,B\subset \mathbb{R}^2 be disjoint sets of size nn and n−3n-3 respectively, with not all of AA contained on a single line. Is there a line which contains at least two points from AA and no points from BB?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/105.lean

Formal Conjectures

FormalConjectures/ErdosProblems/105.leanErdos105.erdos_1053 linesExact file
False ↔  ∀ (A B : Finset (EuclideanSpace ℝ (Fin 2))),    Disjoint A B → A.card = B.card + 3 → ¬Collinear ℝ ↑A → ∃ p ∈ A, ∃ q ∈ A, p ≠ q ∧ ∀ b ∈ B, b ∉ affineSpan ℝ {p, q}
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:105
  • PLBY Lean proofsErdosProblems.Erdos105

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

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