lean_workbook_plus_5978

⚠️ 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.

Show that there are no real numbers $x,y,z$ such that $x,y,z,x+y+z \neq 0$ and $\frac{1}{x+y+z}= \frac{1}{x} + \frac{1}{y} + \frac{1}{z}$ .

Why this node was retired

The posted statement is

theorem lean_workbook_plus_5978 : ¬ (∃ x y z : ℝ, x + y + z ≠ 0 ∧ 1 / (x + y + z) = 1 / x + 1 / y + 1 / z)   :=  by sorry

The source nonzero coordinate conditions were omitted, but restoring them still leaves the source false.

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

Proposed corrected statement

Even with all coordinates nonzero,(x,y,z)=(1,−1,1) satisfies the equality. Correct the source to a positive-coordinate nonexistence statement, or classify its nonzero signed solutions; do not claim that nonzero conditions alone fix it.

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.