Number theory
Approved
The limiting density of the largest subsets of {1, ..., n} in which no element divides two distinct others exists and is irrational. This result addresses part (ii).
Submitted by JenW1N
The PDF is a working mathematical exposition. Lean verification applies to the formal source, not the prose.
f n / n exists and, if so, whether it is
irrational. Formal statement
Proof target
import Mathlib
import FormalConjectures.ErdosProblems.«1062»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos1062.erdos_1062.parts.ii" := by
sorry
end Bounty
Original conjecture (Lean type)
(∃ l, Filter.Tendsto (fun n => ↑(Erdos1062.f n) / ↑n) Filter.atTop (nhds l) ∧ Irrational l) ↔ TrueOriginal conjecture source: FormalConjectures/ErdosProblems/1062.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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Individual lemmas, special cases and supporting work, shown in their original scope.
Nothing has been published against this problem yet.
conjectures-tasks
The pinned statement, the Lean challenge file and the exact bundle you build against.
versions/fc-v2-parts-ii-b8e4a85ac0b7aae1f2867871-formalized →
conjectures-contribution
Every published piece for this problem, with its Lean source and its signed record.
contributions/erdos-1062-parts-ii →