Erdős problem 965 · problems.science

Erdős asks in [Er75b] if for every 2-coloring of ℝ, there is an uncountable set $A ⊆ ℝ$ such that all sums $a + b$ for $a, b ∈ A, a ≠ b$ have the same colour.

Sources

Browse retained paths and inspect the exact material available for this Problem.

2 retained statements2415f78e850a

Open selected source

FormalConjectures/ErdosProblems/

965.lean

Retained formal statement2 of 2

In fact, in both [Ko16] and [SWCol] a generalized example for $k$ -sums is constructed.

FormalConjectures/ErdosProblems/965.leanErdos965.erdos_965.variants.generalization4 linesExact file

1False ↔2  ∀ k ≥ 2,3    ∀ (f : ℝ → Fin 2),4      ∃ A, ¬A.Countable ∧ ∀ (s t : Finset ℝ), ↑s ⊆ A → ↑t ⊆ A → s.card = k → t.card = k → f (s.sum id) = f (t.sum id)

SolvedStatement only, no proof

Sources

Search problems.science