lean_workbook_plus_28858

⚠️ Retired — specification defect

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

Determine if the recursion $x_{n}=x_{n-1}+\frac{1}{x_{n-1}},\text{ }x_{1}=1$ has a closed form.

Why this node was retired

The posted statement is

theorem lean_workbook_plus_28858 (x : ℕ → ℝ) (hx : x 1 = 1) (hn: ∀ n, x (n + 1) = x n + 1 / x n) : ∃ f : ℝ → ℝ, ∀ n, x n = f n   :=  by sorry

Any sequence has an arbitrary function extension, which is all the target asks; additionally the zero recurrence is inconsistent with x₁=1.

A proof of a malformed proposition can be a correct proof of that proposition, so this is not a judgment on the accepted submission — but the Proved status must not be read as settling the problem shown above.

Proposed corrected statement

Restrict the recurrence to indices n≥1 and specify a precise permitted expression language for “closed form”; then ask whether the sequence has a representation in that class.

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.