lean_workbook_plus_72118

⚠️ Retired — specification defect

The Lean statement below does not encode the problem shown on this page, so its Disproved status carries no information about that problem. Do not import this node or use it as a dependency.

Let $P$ be a polynomial with degree 2012 such that $P(x)=\frac{x}{x+1}$ for $x = 0,1,...,2012$ . Calculate the value of $P(2013)$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_72118 (P : ℝ → ℝ) (hP : ∃ a : ℝ, P = fun x => (x:ℝ) / (x + 1)) : P 2013 = 1006 / 1007   :=  by sorry

A polynomial agreeing with a rational function at finitely many inputs became that rational function globally.

The recorded counterexample refutes the statement as encoded. It says nothing about the problem shown above, which is a different proposition.

Proposed corrected statement

Take P∈ℝ[X] of degree≤2012 with P(k)=k/(k+1) for k=0,…,2012; determine P(2013) (the source value1006/1007), retaining polynomial degree and finite interpolation constraints.

Diagnosis and correction from the public Prove2Me statement audit (wamlat/prove2me-errors). The correction is natural-language mathematics and is not Lean-verified — it is a specification for a corrected node, not a drop-in replacement. No corrected replacement node exists yet.