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Re: using N function

• To: mathgroup at smc.vnet.net
• Subject: [mg76336] Re: using N function
• From: dimitris <dimmechan at yahoo.com>
• Date: Sun, 20 May 2007 02:21:37 -0400 (EDT)
• References: <f2me6h$lu4$1@smc.vnet.net>

Watch the differences.

In[34]:=
o = Cos[31^(1/3)]; (*a number very close to -1; see
http://mathworld.wolfram.com/AlmostInteger.html)

Then

In[35]:=
N@o

Out[35]=
-1.

In[36]:=
N@o//InputForm

Out[36]//InputForm=
-0.999999977527746

In[37]:=
o//N[#,MachinePrecision]&//InputForm

Out[37]//InputForm=
-0.999999977527746

But

In[38]:=
o//N[#,$MachinePrecision]&//InputForm

Out[38]//InputForm=
-0.9999999775277460225993505331`15.954589770191003

Almost 16 digits of precision.

Also execute the following command

In[50]:=
FrontEndExecute[{HelpBrowserLookup["MainBook", "3.1.4", "4.14"]}]

You will be gone to a relevant section of Mathematica information with
enough information for understanding their differences!
Note that I don't know if the the last command works in version 6!

Dimitris


 /  kkwweett       :
> 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] - 6403203]
> Out[1]=256.
>
>
> c)
> In[2]:=N[Exp[Sqrt[163 ]Pi] - 6403203,$MachinePrecision]
> Out[2]=743.9999999999993
>
> ?
>
> Thank you