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

• To: mathgroup at smc.vnet.net
• Subject: [mg120032] Re: Numerical accuracy/precision - this is a bug or a feature?
• From: DrMajorBob <btreat1 at austin.rr.com>
• Date: Wed, 6 Jul 2011 05:41:32 -0400 (EDT)

```"Mathematica treat 2.0 as a 2.0+-0.1"

No, it treats it as 2 with machine precision -- almost 16 digits at my
machine -- not two digits, as you're describing.

Bobby

On Tue, 05 Jul 2011 04:12:05 -0500, slawek <slawek at host.pl> wrote:

>
> U=BFytkownik "Kevin J. McCann" <kjm at KevinMcCann.com> napisa=B3 w wiadomo=B6ci
> 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
>
>

--
DrMajorBob at yahoo.com

```

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