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Re: 1^Infinity

  • To: mathgroup at smc.vnet.net
  • Subject: [mg38207] Re: 1^Infinity
  • From: "David W. Cantrell" <DWCantrell at sigmaxi.org>
  • Date: Thu, 5 Dec 2002 03:30:50 -0500 (EST)
  • References: <askfsv$l1n$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Ersek, Ted R" <ErsekTR at navair.navy.mil> wrote:
>  Hello,
>  Consider this:
>
>     In[1]:=
>       1^Infinity
>
>     Out[1]=
>       Indeterminate
>
>  ---------
>  I agree 1.0^Infinity  is Indeterminate because 1.0 might be a bit less
>  than 1 or a bit greater than 1.
>  but isn't  (1*1*1* ..... *1)  simply the integer 1.

Yes, in my opinion. Indeed, I would, arguing similarly, say that
1^x should be 1 for _all_ x, including ComplexInfinity. It is, in
essence, the same idea that I proposed in the recent thread
"indeterminate expression". (Below my signature, I've copied the most
relevant post from that thread.)

At least I can say that Mathematica's returning Indeterminate for both
0^0 and 1^Infinity indicates that it is following a _consistent_
philosophy. But I disagree with that philosophy.

Regards,
 David

On Thursday, November 7, 2002, at 03:05 PM, DWCantrell at aol.com wrote:

> In a message dated 11/06/2002 22:26:25 GMT Standard Time,
> andrzej at platon.c.u-tokyo.ac.jp writes:
>
>>  I think it may not be such a good idea for a programming language to
>>  always return 1 for 0^0.
>
> Allow me to clarify my position. Since this is a Mathematica newsgroup,
> I had assumed that, when I wrote 0, it was understood that I was not
> talking about 0.0 also. I suggest that 0^0 should be 1, just as
> previously. Furthermore, to clarify things, I also suggest that 0.0^0
> should be 1 but that 0^0.0 and 0.0^0.0 should be Indeterminate.
>
> Notes:
> (1) One of the computer algebra systems to which I had alluded earlier
> makes this very type of distinction, based upon whether the exponent
> is 0 or 0.0 .
> (2) Suggesting that the two latter expressions should be Indeterminate
> clearly goes against Kahan's position. He would have them be 1.0
> instead.

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