lean_workbook_plus_40881

⚠️ 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 $[\lfloor{\sqrt{2005}}\rfloor]$ and $[\lfloor{\sqrt[3]{2005}}\rfloor]$

Why this node was retired

The posted statement is

theorem lean_workbook_plus_40881 : ⌊Real.sqrt 2005⌋ = 44 ∧ ⌊(2005:ℝ)^(1/3)⌋ = 12   :=  by sorry

A natural fractional exponent replaces the intended root.

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

Confirmed directly from the Lean text: the numeric-literal exponent carries no type ascription, so it elaborates at type ℕ where division truncates (^(1/3) → ^0).

Proposed corrected statement

Use genuine real cube roots in the second floor; retain the square-root floor 44 and cube-root floor 12 in the exact source expression, with explicit ordinary domain conditions; verify the repaired mathematical claim separately.

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.