       Re: Truth in inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg29363] Re: Truth in inequalities
• From: Erk Jensen <Erk.Jensen at cern.ch>
• Date: Fri, 15 Jun 2001 02:23:35 -0400 (EDT)
• Organization: CERN http://www.cern.ch
• References: <9g9mra\$fpt\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Jack Goldberg wrote:
>
> Hi group,
>
> Can someone explain the logic of the following:
>
>         x < Infinity            returns         x < Infinity
> while
>         x - Infinity < 0        returns         True
>
> I should mention that I am aware of the fact that x - Infinity simplifies
> automatically to -Infinity which is then compared to 0 and found wanting.
> The issue I'm raising is why should a CAS that has  x-Infinity < 0 return
> True not also return True for the  x < Infinity?  One awkwardness of
> having this difference of behavior can be seen in the example,
>
> MyFunction[x_,y_]/;(x<y) :=  blah
>
> and
>
> MyFunction[x_,y_]/;(x-y<0)  := blah
>
> do not do the same thing when, say, y=Infinity.
>
> Just curious :-)
>
> Jack

Have you noticed that both
Simplify[x < \[Infinity], x \[Epsilon] Reals]
and
Simplify[Abs[x] < \[Infinity]]
result in "True"?

x-\[Infinity] resolves immediately to -\[Infinity] which I think it
shouldn't, since if x is equal to \[Infinity], the result should be
'Indeterminate'.

Evaluate these three lines and you'll see what I mean:
Simplify[(x - y) /. {x -> \[Infinity], y -> \[Infinity]}]
Simplify[(x - y) /. {x -> \[Infinity]} /. {y -> \[Infinity]}]
Simplify[(x - y) /. {y -> \[Infinity]} /. {x -> \[Infinity]}]

Ciao
-erk-
--
Dr.-Ing. Erk JENSEN                    mailto:Erk.Jensen at cern.ch
CERN  PS/RF  L19510          http://jensene.home.cern.ch/jensene
CH-1211 Geneva 23                      Tel.:     +41 22 76 74298
Switzerland                            Fax.:     +41 22 76 78510

```

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