Re: )

*To*: mathgroup at smc.vnet.net*Subject*: [mg66313] Re: )*From*: Maxim <m.r at inbox.ru>*Date*: Tue, 9 May 2006 02:35:08 -0400 (EDT)*References*: <200605050902.FAA28575@smc.vnet.net> <e3hf84$m1h$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Sat, 6 May 2006 06:20:52 +0000 (UTC), Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > > laws of arithmetic do not hold). Some of them are hard to explain: I > can't see any good reason at all why Infinity^Infinity is > ComplexInfinity, and it seems to contradict the the most basic rule > that x^y is always real when x and y are positive reals. Besides, as > I mentioned earlier, Infinity and ComplexInfinity do not belong > together in any topological model known to me (you need a > "topological model" to be able to consider the issue of continuity) > and should never appear in the same formula. I can only consider this > as a bug, and a rather silly one. > I think this is as it should be: we need to consider all the sequences converging to Infinity, and, for example, Limit[(x + I*Pi)^x, x -> Infinity] == -Infinity. So in that sense Infinity^Infinity == ComplexInfinity: when z = z1^z2 and z1, z2 go to Infinity the absolute value of z always tends to Infinity but the argument can be arbitrary. Maxim Rytin m.r at inbox.ru

**Follow-Ups**:**Re: Re: )***From:*Andrzej Kozlowski <akoz@mimuw.edu.pl>

**References**:**When is x^y = != E^(y*Log[x])***From:*ted.ersek@tqci.net