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MathGroup Archive 1999

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Re: RE: Sort

  • To: mathgroup at smc.vnet.net
  • Subject: [mg19278] Re: [mg19188] RE: Sort
  • From: "Tomas Garza" <tgarza at mail.internet.com.mx>
  • Date: Thu, 12 Aug 1999 01:24:29 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

Ersek, Ted R [ErsekTR at navair.navy.mil] wrote:

> I discovered something related behavior
> Hermann Meier noted about Sort.
> -------------------
> Sort, Union, Intersection, and Complement each
> return a "sorted" list in the examples below, but
> the lists aren't sorted according to their
> numeric value.
>
>
> In[1]:=
> Sort[{0,-3,-Pi,5,Pi/2}]
>
> Out[1]=
> {-3, 0, 5, -Pi, Pi/2}
>
>
> In[2]:=
> Union[{0,-3,-Pi,5,Pi/2}]
>
> Out[2]=
> {-3, 0, 5, -Pi, Pi/2}
>
>
> In[3]:=
> Intersection[{-3,5,-Pi},{-3,0,5,-Pi,Pi/2}]
>
> Out[3]=
> {-3, 5, -Pi}
>
>
> In[4]:=
> Complement[{-3,0,5,-Pi,Pi/2},{0,Pi/2,6,8}]
>
> Out[4]=
> {-3, 5, -Pi}
>
> -----------------------
>
> I am pretty sure the lists above are sorted
> by the method described in Section A.3.9 in
> The Mathematica Book.

I think it is best to start by explaining that Pi is a symbol:

In[1]:=
Head[Pi]
Out[1]=
Symbol

One should not confuse Pi with Pi//N:

In[2]:=
Sort[{0, -3, -Pi // N, 5, Pi/2 // N}]

Out[2]=
{-3.14159, -3, 0, 1.5708, 5}

The result here agrees with what one would expect if all the elements to be
sorted were numbers. No strange results thus far.

Tomas Garza
Mexico City



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