Re: One to the power Infinity
- To: mathgroup at smc.vnet.net
- Subject: [mg35952] Re: One to the power Infinity
- From: "John Jowett" <John.Jowett at cern.ch>
- Date: Fri, 9 Aug 2002 05:18:00 -0400 (EDT)
- Organization: CERN
- References: <aitfon$cfu$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
<Matthias.Bode at oppenheim.de> wrote in message news:aitfon$cfu$1 at smc.vnet.net... > Dear Colleagues, > > when fooling around with MATHEMATICA I found: > > 0^\[Infinity] => 0, as expected; > 0.9^\[Infinity] => 0, as expected; > 2^\[Infinity] => Infinity, as expected; > 1^\[Infinity] => Indeterminate, unexpected. Naively expected: 1. > > For which reason(s) is 1^\[Infinity] defined as Indeterminate? Matthias, In only slightly sloppy language, you might consider this as the limit as x -> 0 from above of either (1+x)^\[Infinity] or (1-x)^\[Infinity] For any small positive x, these expressions are Infinity or 0 respectively so it is pretty clear that the limit has to be indeterminate. John Jowett http://cern.ch/jowett/