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Re: Re: Re: FindRoot cannot find obvious solution

  • To: mathgroup at
  • Subject: [mg48129] Re: [mg48092] Re: [mg48085] Re: FindRoot cannot find obvious solution
  • From: Andrzej Kozlowski <akoz at>
  • Date: Fri, 14 May 2004 00:12:27 -0400 (EDT)
  • References: <> <c6o3lc$cd0$> <c6qags$s56$> <> <c7klcs$2kn$> <> <> <>
  • Sender: owner-wri-mathgroup at

On 13 May 2004, at 23:26, Daniel Lichtblau wrote:
> The issue of 1`2==2.2 is a bit dicey. I believe the most useful 
> interpretation is roughly as Andrzej suggests, that the model breaks 
> down at sufficiently low precision. Yes, there are "contradictions" is 
> the logic that lead to the equality above, but to me they are not 
> terribly compelling.
> Daniel
At least in this respect Mathemaitca's behaviour agrees with the 
documentation: since



has only 7 digits it does "differ in at most last eight binary digits" 
from 2.

This is a bit more tricky

1.`2 == 0




The key point is clearly the fact that here Sin slightly increases 



Looking at RealDigits[Sin[1`2],2] is not quite convincing, since 
Mathematica still returns only 7 digits:



but I suspect that the statement in the documentation about "last eight 
binary digits" is also only approximate and that this is actually a 
border line case (just over the border line).

In any case, these are clearly pathologies of significance arithmetic 
and without importance.

Andrzej Kozlowski
Chiba, Japan

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