39.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

1 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 39

Reference: erdosproblems.com/39

Imports (1)

FormalConjecturesUtil

theorem Erdos39.erdos_39 Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}$ for all $\varepsilon > 0$? sorry line 38 source
Source documentation
Is there an infinite Sidon set $A\subset \mathbb{N}$ such that $\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}$ for all $\varepsilon > 0$?

depends on sorry what this means
Statement uses: Iff, True, Exists, Set, Nat, And, Set.Infinite, IsSidon, Real, GT.gt, OfNat.ofNat, Asymptotics.IsBigO, Filter.atTop, HPow.hPow, HSub.hSub, HDiv.hDiv, Set.ncard, Inter.inter, Set.Icc
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
44 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_39 : answer(sorry) ↔ ∃ (A : Set ℕ), A.Infinite ∧ IsSidon A ∧
    ∀ᵉ  (ε  > (0 : ℝ)),
    (· ^ (1 / 2 - ε) : ℕ → ℝ) =O[atTop] fun N => (((Set.Icc 1 N) ∩ A).ncard : ℝ) := by
…
```
Mentions: IsSidon