749.lean`

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 749

Reference: erdosproblems.com/749

Imports (1)

FormalConjecturesUtil

theorem Erdos749.erdos_749 Let $\epsilon>0$ sorry line 38 source
Source documentation
Let $\epsilon>0$. Does there exist $A\subseteq \mathbb{N}$ such that the lower density of $A+A$ is at least $1-\epsilon$ and yet $1_A\ast 1_A(n) \ll_\epsilon 1$ for all $n$?

depends on sorry what this means
Statement uses: Iff, True, Real, GT.gt, OfNat.ofNat, Exists, Set, Nat, And, LE.le, HSub.hSub, Set.lowerDensity, HAdd.hAdd, Set.univ, Asymptotics.IsBigO, Filter.atTop, Function.comp, AdditiveCombinatorics.sumRep
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
37 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_749 : answer(sorry) ↔ ∀ ε > (0 : ℝ),
    ∃ A : Set ℕ, 1 - ε ≤ lowerDensity (A + A) ∧
    ((Nat.cast (R := ℝ) ∘ sumRep A) ≪ (fun n => (1: ℝ))) := by
…
```