lean_workbook_plus_33524

⚠️ 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 $x \in \mathbb{R}$ , $0< x < 1$ . Show that there exist integers $a_1, \ldots, a_n, \ldots$ such that $0 \leq a_n \leq 9$ and $x = \frac{a_1}{10} + \frac{a_2}{10^2} + \ldots + \frac{a_n}{10^n} + \ldots$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_33524 (x : ℝ) (hx: 0 < x ∧ x < 1) : ∃ (a : ℕ → ℕ), (∀ n:ℕ, 0 ≤ a n ∧ a n ≤ 9) ∧ (x = ∑' n:ℕ, a n / 10 ^ n )   :=  by sorry

Compute the series in ℝ: x=∑n:ℕ,(a n:ℝ)/10^(n+1), with each a n a decimal digit. This uses zero-based indexing for the source digits a₁,a₂,….

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

Proposed corrected statement

Compute the series in ℝ: x=∑n:ℕ,(a n:ℝ)/10^(n+1), with each a n a decimal digit. This uses zero-based indexing for the source digits a₁,a₂,….

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.