Erdős ProblemsMeasure and integration
Erdős Problem 1038: I
What is the infimum of |{x ∈ ℝ : |f x| < 1}| over all nonconstant monic polynomials f such that all of its roots are real and contained in [-1,1]?
Mathematical statement
What is the infimum of |{x ∈ ℝ : |f x| < 1}| over all nonconstant monic polynomials f such
that all of its roots are real and contained in [-1,1]?
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_1038.parts.i
theorem erdos_1038.parts.i (n : ℕ) : answer(sorry) = ⨅ f : {f : Polynomial ℝ // f.Monic ∧ f ≠ 1 ∧ (f.roots.filter fun x => x ∈ Set.Icc (-1 : ℝ) 1).card = f.natDegree}, volume {x | |f.1.eval x| < 1} := 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