Erdős Problem #229
PROVED LEANdatabase updated 2025-12-28
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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Let \((S_n)_{n \ge 1}\) be a sequence of sets of complex numbers, none of which have a finite limit point. Does there exist an entire transcendental function \(f(z)\) such that, for all \(n \ge 1\), there exists some \(k_n \ge 0\) such that \(f^{(k_n)}(z) = 0\) for all \(z \in S_n\). This is Problem 2.30 in [Ha74], where it is attributed to Erdős. Solved in the affirmative by Barth and Schneider [BaSc72]. This was formalized in Lean by Alexeev using Aristotle.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/229.Prizenone
Topicsanalysis, iterated functions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/229
Attempts
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