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. -- -------------------- http://NewsReader.Com/ -------------------- Usenet Newsgroup Service New Rate! $9.95/Month 50GB
- Follow-Ups:
- Re: Re: 1^Infinity
- From: Selwyn Hollis <selwynh@earthlink.net>
- Re: Re: 1^Infinity