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Re: Infinity vs DirectedInfinity[1]

• To: mathgroup at smc.vnet.net
• Subject: [mg70562] Re: [mg70489] Infinity vs DirectedInfinity[1]
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 19 Oct 2006 03:23:37 -0400 (EDT)
• References: <200610180816.EAA07979@smc.vnet.net>

On 18 Oct 2006, at 17:16, Chris Chiasson wrote:

> Infinity is a symbol, as far as I know. However, in FullForm it is
> shown as the equivalent DirectedInfinity[1].
>
> Is there some kind of MakeBoxes rule for FullForm that makes Infinity
> show up that way?
>
> --  
> http://chris.chiasson.name/
>

In fact this is not quite true. Observe:

In[1]:=
FullForm[Hold[Infinity]]

Out[1]//FullForm=
Hold[Infinity]

In[2]:=
FullForm[Infinity]

Out[2]//FullForm=
DirectedInfinity[1]

What happens is that the symbol Infinity evaluates to DirectedInfinity 
[1]. This kind of thing is not uncommon in Mathematica; e.g. 2+3 I  
evaluates to Complex[2,3] or 2/3 evaluates to Rational[2,3]. All this  
is purely Kernel stuff; no MakeBoxes involved.

Andrzej Kozlowski
Tokyo, Japan

• References:
  • Infinity vs DirectedInfinity[1]
    • From: "Chris Chiasson" <chris@chiasson.name>