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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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