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.

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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.

In [Ko16] Péter Komjáth constructed a counterexample. The same result was proven independently in [SWCol] by Sokoup and Weiss.

FormalConjectures/ErdosProblems/965.leanErdos965.erdos_9651 lineExact file

1False ↔ ∀ (f : ℝ → Fin 2), ∃ A, ¬A.Countable ∧ ∀ a ∈ A, ∀ b ∈ A, ∀ c ∈ A, ∀ d ∈ A, a ≠ b → c ≠ d → f (a + b) = f (c + d)

SolvedStatement only, no proof

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