lean_workbook_plus_49919

⚠️ 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.

Find all continuous functions $f\colon \mathbb({0;+\infty)}\to\mathbb({0;+\infty)}$ such that $f(x)f(y)=f(xy)+f(\frac{x}{y})$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_49919 (f : ℝ → ℝ) (hf: Continuous f) (hx: ∀ x y : ℝ, (x>0 ∧ y>0) → f x * f y = f (x*y) + f (x/y)) : ∀ x : ℝ, x>0 → f x = x   :=  by sorry

The complete intended solution family is not established by this audit.

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

Proposed corrected statement

Restore the task of classifying continuous positive-valued functions on(0,∞) satisfying the displayed equation; remove the invented answer f(x)=x. The constant function2 must be admitted.

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.