Re: Re: Re: FindRoot cannot find obvious solution
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- Subject: [mg48129] Re: [mg48092] Re: [mg48085] Re: FindRoot cannot find obvious solution
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 14 May 2004 00:12:27 -0400 (EDT)
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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.
At least in this respect Mathemaitca's behaviour agrees with the
has only 7 digits it does "differ in at most last eight binary digits"
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.
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