Back to Problems

union_closed.variants.sharpness

Specification

The union-closed sets conjecture is sharp in the sense that if we replace the constant `1/2` with any larger constant, then the conjecture fails.

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof
Lean 4 Statement 
theorem union_closed.variants.sharpness [Fintype n] (c : ℝ) (hc : 1 / 2 < c) :
    ¬ (∀ A : Finset (Finset n), A ≠ {∅} → IsUnionClosed A →
        ∃ i : n, c * #A ≤ #{x ∈ A | i ∈ x})
ID: Wikipedia__UnionClosed__union_closed.variants.sharpness
Browse 300 unsolved math conjectures formalized in Lean 4
Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →
ASI Prize documentation for formal verification pipeline
Docs

Verification Pipeline

How zero-trust verification works.

Read docs →
Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.