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
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