1029.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 1029

References:

erdosproblems.com/1029
[Er93] Erdős, Paul, Some of my favorite solved and unsolved problems in graph theory. Quaestiones Math. (1993), 333-350.
[ErSz35] Erdős, P. and Szekeres, G., A combinatorial problem in geometry. Compos. Math. (1935), 463-470.
[Sp75] Spencer, J., Ramsey's theorem - a new lower bound. J. Combin. Theory Ser. A (1975), 108-115.

Imports (1)

FormalConjecturesUtil

theorem Erdos1029.erdos_1029 Documented declaration: erdos_1029 sorry line 48 source
Source documentation
If $R(k)$ is the Ramsey number for $K_k$, the minimal $n$ such that every $2$-colouring of the edges of $K_n$ contains a monochromatic copy of $K_k$, then $$\frac{R(k)}{k2^{k/2}}\to \infty.$$
In [Er93] Erdős offers $100 for a proof of this and $1000 for a disproof, but says 'this last offer is to some extent phoney: I am sure that this is true (but I have been wrong before).'

depends on sorry what this means
Statement uses: Filter.Tendsto, Nat, Real, HDiv.hDiv, SimpleGraph.diagonalRamsey, HMul.hMul, HPow.hPow, OfNat.ofNat, Filter.atTop
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
30 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem erdos_1029 :
    Tendsto (fun k : ℕ ↦ (SimpleGraph.diagonalRamsey k : ℝ) /
      ((k : ℝ) * (2 : ℝ) ^ ((k : ℝ) / 2))) atTop atTop := by
…
```
Mentions: SimpleGraph.diagonalRamsey