Combinatorics
A be an infinite B₂[2] set. Must liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0? $5,103 bounty
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«158»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos158.erdos_158" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (A : Set ℕ),
A.Infinite → Erdos158.B2 2 A → Filter.liminf (fun N => ↑(A ∩ Set.Iio N).ncard * ↑N ^ (-1 / 2)) Filter.atTop = 0Original conjecture source: FormalConjectures/ErdosProblems/158.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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