Re: Re: indeterminate expression
- To: mathgroup at smc.vnet.net
- Subject: [mg37671] Re: [mg37606] Re: indeterminate expression
- From: DWCantrell at aol.com
- Date: Fri, 8 Nov 2002 02:14:45 -0500 (EST)
- Sender: owner-wri-mathgroup at wolfram.com
In a message dated 11/07/2002 15:14:42 GMT Standard Time, andrzej at tuins.ac.jp writes: > I am not "strongly" against your suggestion, but I am wondering if > there may not be situation when someone would find it inconvenient. > For example, consider the following (admittedly rather contrived) > example. I have nothing against contrived examples. :-) > Suppose you have an expression p=a1^n1*a2^n2*... where all ai > and ni are functions of x. Setting x to 0 and checking that you get a > non-zero answer you can now conclude that a1,a2,a3 ... are all > non-zero at x=0. Not quite. ComplexInfinity is certainly a non-zero answer, and of course 0^(-1) gives ComplexInfinity. I suppose you had intended to say "...get a _finite_ non-zero answer..." Then such a conclusion would be valid now in Mathematica, but would not be valid if the change I suggested were to be implemented. So the point you've raised is worth considering. FWIW, going slightly "off on a tangent" (since it's not directly related to the 0^0 issue), finding that p=a1^n1*a2^n2*...*aN^nN _does_ equal 0 does _not_ allow us to conclude that some ai must be 0 (since, for example, (1/2)^(+Infinity) = 0). Note that, if infinities were outlawed (which I certainly do not recommend!!), then we would be able to say neatly that, if all ni are positive, a1^n1*a2^n2*...*aN^nN = 0 iff some ai = 0. It looks nice. But the price for getting it is too high. David > If 0^0 was 1 you would not longer be able to do that. What I > really mean to say is that 1 obtained as 0^0 may not for all purposes > be "as good" as 1 obtained in a more normal way. I am sure this sort > of problem would be rare but I suspect eventually someone would write > to the mathgroup to complain about it :) > > Andrzej > > > 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.