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Why Mathematica does not issue a warning when the calculations are losing so much precision that the results are not anymore useful?

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  • Subject: [mg117499] Why Mathematica does not issue a warning when the calculations are losing so much precision that the results are not anymore useful?
  • From: John Travolta Sardus <pireddag at hotmail.com>
  • Date: Mon, 21 Mar 2011 06:13:24 -0500 (EST)

With Mathematica 8.0.1

N[FractionalPart[(6 + Sqrt[2])^20]]

Result:

-160.

Is it a problem for all numerical software being able to recognize when 
these calculations cannot be performed with the given machine accuracy? 
Does this happen in this case only (where a wrong result is easily 
recognized) or in other cases too?

Thanks for any answer,

Giovanni


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