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Re: Numerical accuracy/precision - this is a bug or a feature?

• To: mathgroup at smc.vnet.net
• Subject: [mg120016] Re: Numerical accuracy/precision - this is a bug or a feature?
• From: "slawek" <slawek at host.pl>
• Date: Tue, 5 Jul 2011 05:12:05 -0400 (EDT)
• References: <ius5op$2g7$1@smc.vnet.net> <ius7b6$30t$1@smc.vnet.net>

U¿ytkownik "Kevin J. McCann" <kjm at KevinMcCann.com> napisa³ w wiadomo¶ci grup 
dyskusyjnych:ius7b6$30t$1 at smc.vnet.net...
> The answer to this puzzle is that the N[2.0,20] is 2.0, not
> 2.00000000... Try N[2,20] and all is well. I think that when you put 2.0
> in you have already limited yourself to machine precision, and N[2.0,20]
> is then just machine accuracy.

It is still a-bug-and-a-feature.
And this bug make Mathematica nearly useless in numerical computations. "MS 
Windows Calculator" is much more reliable!


The number of written digits IS NEITHER the precision NOR the accuracy. 
Mathematica treat 2.0 as a 2.0+-0.1, but it is not the proper way to handle 
numbers.

I know, that it is common mistake to treat 2.0 as "not an integer number" 
and/or "exact" number, but 2.0 is an integer number AND also it is a 
rational number AND also a real number AND also a complex number. And 2.0 is 
simply 1+1+ 0/10 . Therefore, as you see, there is no "roudning", "limited 
precision", "error" or "uncertinaity". It is only a matter of a notation of 
decimal fractions. And decimal fractions are exact. Any "tolerance" is not 
indicated in any way by this notation. Thus it is a bug. Nasty, big, fat bug 
in the core of Mathematica.

Even from "CS view" 2.0 is translated to IEEE representation with 56-bits of 
the mantisa. Nobody declare float x = 2.0000000000 to iniject the float 
point two into a code.

slawek