Erdős problem 846
Erdős Problem 846 Let A ⊂ ℝ² be an infinite set for which there exists some ϵ>0 such that in any subset of A of size n there are always at least ϵn with no three on a line. Is it true that A is the union of a finite number of sets where no three are on a line?
Sources
FormalConjectures/ErdosProblems/
846.lean
Retained formal statement
Erdős Problem 846 Let A ⊂ ℝ² be an infinite set for which there exists some ϵ>0 such that in any subset of A of size n there are always at least ϵn with no three on a line. Is it true that A is the union of a finite number of sets where no three are on a line?
In other words, prove or disprove the following statement: every infinite ε-non-trilinear subset of the plane is weakly non-trilinar.
False ↔ ∀ (A : Set (EuclideanSpace ℝ (Fin 2))), ∀ ε > 0, A.Infinite → Erdos846.NonTrilinearFor A ε → Erdos846.WeaklyNonTrilinear A