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Erdős ProblemsCombinatorics

Erdős Problem 624

Let XX be a finite set of size nn and H(n)H(n) be such that there is a function f:{A:A⊆X}→Xf:\{A : A\subseteq X\}\to X so that for every Y⊆XY\subseteq X with ∣Y∣≥H(n)\lvert Y\rvert \geq H(n) we have {f(A):A⊆Y}=X\left\{ f(A) : A\subseteq Y\right\}=X. Prove that $H(n)-\log_2 n \to \in...

CombinatoricsAMS 5

Mathematical statement

Let XX be a finite set of size nn and H(n)H(n) be such that there is a function f:{A:A⊆X}→Xf:\{A : A\subseteq X\}\to X so that for every Y⊆XY\subseteq X with ∣Y∣≥H(n)\lvert Y\rvert \geq H(n) we have {f(A):A⊆Y}=X\left\{ f(A) : A\subseteq Y\right\}=X. Prove that H(n)−log⁡2n→∞H(n)-\log_2 n \to \infty.

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_624

Canonical source
Complete statement target, proof intentionally absentLean 4
theorem erdos_624 :    atTop.Tendsto (fun n : ℕ => H n - Real.logb 2 (n : ℝ)) atTop := 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 sourceformalizationerdosproblems.com/624background