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MathGroup Archive 2006

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Re: Correction re. 1`2 == 1*^-10

  • To: mathgroup at smc.vnet.net
  • Subject: [mg71559] Re: [mg71526] Correction re. 1`2 == 1*^-10
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Thu, 23 Nov 2006 05:41:29 -0500 (EST)
  • References: <200611221022.FAA04447@smc.vnet.net>

There are many very strange effects when using low precision (or
accuracy) numbers in Mathematica. I don't have a way to explain this
one.

On 11/22/06, Andrew Moylan <andrew.j.moylan at gmail.com> wrote:
> In my original message (below), I wrote "I've resolved my sorting
> problem by using OrderedQ instead of Less as the ordering function in
> Sort". Instead of "OrderedQ" I should have written
> "OrderedQ[{SetPrecision[#1, Infinity], SetPrecision[#2, Infinity]}] &".
>
> I previously wrote:
>
> Hi all,
>
> Please help me understand the following behaviour, which was wrecking
> havoc the results I get from calling the function Sort:
>
> Evaluating
>   1`2 == 1*^-10
> gives
>   True
>
> Correspondingly, evaluating each of
>   1`2 < 1*^-10
> and
>   1`2 > 1*^-10
> give
>   False
>
> Can anyone explain why these two numbers are declared to be equal? It's
> inconsistent with my previous understanding of how arbitrary-precision
> numbers are interpreted in Mathematica.
>
> (I've resolved my sorting problem by using OrderedQ instead of Less as
> the ordering function in Sort. But why was this necessary?)
>
> Cheers,
> Andrew
>
>


-- 
http://chris.chiasson.name/


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