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Re: Using N function

• To: mathgroup at smc.vnet.net
• Subject: [mg76281] Re: [mg76270] Using N function
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sat, 19 May 2007 04:30:07 -0400 (EDT)
• References: <200705181031.GAA13821@smc.vnet.net>

On 18 May 2007, at 19:31, kkwweett wrote:

>
> Good morning Mathematica users,
>
>
> Can anyone tell me, please, which of a),b) or c) is wrong :
>
> a)
> <MathematicaHelp>
> <quote>
>
> N[expr] is equivalent to N[expr, MachinePrecision].
>
> </quote>
> </MathematicaHelp>
>
> b)
> In[1]:=N[Exp[Sqrt[163 ]Pi] - 640320^3]
> Out[1]=256.
>
>
> c)
> In[2]:=N[Exp[Sqrt[163 ]Pi] - 640320^3,$MachinePrecision]
> Out[2]=743.9999999999993
>
> ?
>
> Thank you
>

$MachinePrecision and MachinePrecision are different. The first is a  
number (evaluate it on your platform); on my I get:

In[21]:= $MachinePrecision
Out[21]= 15.9546

So N[ ,$MachinePrecision] is essenitally N[ ,16] - quite different  
forn N[] which is N[ ,MachinePrecision].

  N[Exp[Sqrt[163] Pi] - 640320^3, MachinePrecision]
  256.

  N[Exp[Sqrt[163] Pi] - 640320^3, $MachinePrecision]
743.9999999999993

Moral: $ still matters.

Andrzej Kozlowski

• References:
  • Using N function
    • From: kkwweett <kkwweett@hotmail.fr>