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MathGroup Archive 2007

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Re: 1>0 gives False

  • To: mathgroup at smc.vnet.net
  • Subject: [mg73797] Re: [mg73758] 1>0 gives False
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Wed, 28 Feb 2007 04:43:07 -0500 (EST)
  • References: <200702271054.FAA24273@smc.vnet.net>


On 27 Feb 2007, at 11:54, dh wrote:

>
>
> $Version: 5.1 for Microsoft Windows (October 25, 2004)
>
> Hello,
>
> can anyone explain the following:
>
> 1`2 > 0
>
> False
>
> If we have 3 digits of precision: 1`3 we get the correct result.
>
> Daniel
>
>
>

This has come up a number of times so I don't want to repeat this  
here yet agian. See, for example,

http://forums.wolfram.com/mathgroup/archive/2006/Feb/msg00088.html

Note that:


1`2 ==0

so

True

1`2 > 0

False

This is a quirky aspect of significance arithemtic at very low  
precision. The solution is to avoid it. Significance arithmetic is  
intended for high precision computations which can serve as a  
substitute for exact computations when these are too slow to be  
realistic. Low precision numbers like 1'2 ar enot intended to model  
low precision empirical computations and are actually quite useless  
when used for this purpose. One should instead use machine precision  
numbers (or exact numbers when possible) and use bona fide Interval  
aritmetic to estimate errors, if that is needed.

Andrzej Kozlowski





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