Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?

• To: mathgroup at smc.vnet.net
• Subject: [mg64173] Re: SetPrecision causes logical comparisons to fail in Mathematica 5.1 on Mac OS X?
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Fri, 3 Feb 2006 01:58:20 -0500 (EST)
• Organization: The University of Western Australia
• References: <200601251345.IAA25867@smc.vnet.net> <dra3g3\$m55\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```In article <dra3g3\$m55\$1 at smc.vnet.net>,
Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote:

> A partial explanation is given in the documentation for Equal:
>
> "Approximate numbers are considered equal if they differ in at most
> their last eight binary digits (roughly their last two decimal digits)."

There is a subtlety here: clearly

RealDigits[1.101`2, 2]

and

RealDigits[1`2, 2]

do differ in their "last eight" binary digits (actually, in both cases
there are only seven binary digits). The sublety is that all following
(suppressed) binary digits are 0.

> The workaround is never to set anything to have so few digits of
> precision; there is no reason at all to do so. Mathematica's
> "significance" arithmetic is an approximation to true interval
> arithmetic that works well only at high precision.

But if the application is fixed precision arithmetic then one could use
RealDigits (in base 2 or 10). For example,

RealDigits[1.101`2, 2] == RealDigits[1`2, 2]

RealDigits[1.101`2] == RealDigits[1`2]

> If you only wanted to reduce the number of digits displayed you
> should use
>
> NumberForm[1.101, 2]

Or set the PrintPrecision options using the Option Inspector.

Cheers,
Paul

_______________________________________________________________________
Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)
AUSTRALIA                               http://physics.uwa.edu.au/~paul

```

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