Source labels openChecked July 26, 2026

Erdős Problem 101

Given $n$ points in $\mathbb{R}^2$ , no five of which are on a line, the number of lines containing four points is $o(n^2)$ .

Convex geometry AMS 52

Mathematical statement

Given $n$ points in $\mathbb{R}^2$ , no five of which are on a line, the number of lines containing four points is $o(n^2)$ .

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_101

Canonical source

Complete statement target, proof intentionally absentLean 4

theorem erdos_101 : (fun n => (numLinesWithFourPointMax n : ℝ)) =o[atTop] (fun n => (n : ℝ)^2) := 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 sourceformalization erdosproblems.com/101background