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Erdős problem 501

For every x∈Rx \in \mathbb{R} let Ax⊂RA_x \subset \mathbb{R} be a bounded set of Lebesgue outer measure <1< 1. Must there be an infinite independent set, that is an infinite X⊆RX \subseteq \mathbb{R} with x∉Ayx \notin A_y for all distinct x,y∈Xx, y \in X?

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

Retained declaration

FormalConjectures/ErdosProblems/501.lean

Formal Conjectures

FormalConjectures/ErdosProblems/501.leanErdos501.erdos_5014 linesExact file
True ↔  ∀ (A : ℝ → Set ℝ),    (∀ (x : ℝ), Bornology.IsBounded (A x)) →      (∀ (x : ℝ), MeasureTheory.volume.toOuterMeasure (A x) < 1) → ∃ X, X.Infinite ∧ X.Pairwise fun x y => x ∉ A y
OpenStatement only, no proof

Reported activity

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

  • AI collaborating with humans

    Erdős AI contributions wiki · 29 May-1 Jun, 2026

    Machine
    GPT-5.5 Pro
    People
    Sungchul Lee
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  • argument

    VibeMathed

    Machine
    Sol, Claude
    People
    Elliot Glazer
    Reported outcome
    resolved
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