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:::I did not put an absolute value into my version of the definition because if I had, then ''x''<sub>''n''</sub> could not be expressed as a function of ε<sub>''n''</sub> (unless we assume that ''x''<sub>''n''</sub>≥√''S'') which would interfere with deriving the formula for ε<sub>''n''+1</sub>.
:::Also, <math>\vert \frac{x_n}{\sqrt{S}} - 1 \vert</math> is the wrong way to equate over-estimates with under-estimates. Better would be <math>\vert \ln \frac{x_n}{\sqrt{S}} \vert</math>, but I did not want to use the transcendental function ln in an article targeted to a middle school audience. Notice that if ''y''=''S''/''x'', then (''y''+(''S''/''y''))/2=(''x''+(''S''/''x''))/2. So, if ''x'' were an under-estimate of √''S'', then the equivalent over-estimate is ''S''/''x''. If we replace that in the formula for relative error, we get <math>\varepsilon_n = \frac{\frac{S}{x_n}}{\sqrt{S}} - 1 = \frac{\sqrt{S}}{x_n} - 1 </math>. So we could use <math>\varepsilon_n = \max\left(\frac{x_n}{\sqrt{S}},\frac{\sqrt{S}}{x_n}\right) - 1</math> except for the fact that this function is not invertible. [[User:JRSpriggs|JRSpriggs]] ([[User talk:JRSpriggs|talk]]) 08:54, 15 July 2013 (UTC)
== Regarding Vedic Method ==
Is it just me, or are there others who think that the Vedic method can be bettered by some exposition. While the algorithmic side is substantial, I am at loss on why it even works. ([[User:Manoguru|Manoguru]] ([[User talk:Manoguru|talk]]) 03:56, 17 December 2013 (UTC))
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