Re: Mathematica goes Bad
- To: mathgroup at smc.vnet.net
- Subject: [mg59489] Re: Mathematica goes Bad
- From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
- Date: Wed, 10 Aug 2005 02:58:38 -0400 (EDT)
- References: <dd9n09$iuh$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
"Igor Touzov" <igor at nc.rr.com> wrote:
[snip]
> Not to mention it gives you some absurd results as well:
>
> In version 5.0 computing following
>
> {Limit[ArcTan[k ], k -> + [Infinity], Direction -> -1],
> Limit[ArcTan[k ], k -> + [Infinity], Direction -> 1]} results in accurate
>
> {-(Pi/2), Pi/2}
>
> while doing the same in version 5.2 gives you absurd {(Pi/2), Pi/2}.
Perhaps you are confusing Infinity with ComplexInfinity. Note that
In[7]:= Limit[ArcTan[k], k -> ComplexInfinity, Direction -> -1]
Out[7]= -(Pi/2)
In[8]:= Limit[ArcTan[k], k -> ComplexInfinity, Direction -> 1]
Out[8]= Pi/2
using version 5.1 . Since ComplexInfinity has no direction associated
with it, we are at liberty to specify Direction when asking for the
limits, and the results are correct. But Infinity _already_ has an
associated direction
In[9]:= FullForm[Infinity]
Out[9]//FullForm= DirectedInfinity[1]
and thus it is at least strange to specify an optional Direction when
asking for a limit as k -> Infinity. Any optional Direction must be either
superfluous or contradictory to Infinity's innate direction. It seems
reasonable that Mathematica would therefore ignore any optional Direction
specification, and so I like the results given by the more recent versions.
However, I suggest that it might be nice, when asked for
Limit[ArcTan[k], k -> Infinity, Direction -> -1], if Mathematica preceded
its result of Pi/2 with a warning. It could say something like
"Optional Direction ignored; direction used is that of the specified
DirectedInfinity."
David