{"schema":"vela.problem-packet.v0.1","problem":846,"statement":"Let $A\\subset \\mathbb{R}^2$ be an infinite set for which there exists some $\\epsilon>0$ such that in any subset of $A$ of size $n$ there are always at least $\\epsilon n$ with no three on a line.Is it true that $A$ is the union of a finite number of sets where no three are on a line?","status":"solved","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[{"verdict":"faithful","attestedBy":"reviewer:will-blair","formalRef":"erdos_846.lean","targetFinding":"vf_9e571c292bedde14"}],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}