{"schema":"vela.problem-packet.v0.1","problem":1151,"statement":"Given $a_1,\\ldots,a_n\\in [-1,1]$ let\\[\\mathcal{L}^nf(x) = \\sum_{1\\leq i\\leq n}f(a_i)\\ell_i(x)\\]be the unique polynomial of degree $n-1$ which agrees with $f$ on $a_i$ for $1\\leq i\\leq n$ (that is, the Lagrange interpolation polynomial).Let $a_i$ be the set of Chebyshev nodes. Prove that, for any closed $A\\subseteq [-1,1]$, there exists a continuous function $f$ such that $A$ is the set of limit points of $\\mathcal{L}^nf(x)$.","status":"open","seam":"raw","closureRoutes":[],"obligations":[],"attestations":[],"attempts":[],"velaLean":[],"oeis":[],"generated_note":"derived view; the signed event log is the source of truth (vela check / vela reproduce)"}