Re: weird Log[0] *0 result

*To*: mathgroup at smc.vnet.net*Subject*: [mg9060] Re: [mg9022] weird Log[0] *0 result*From*: Olivier Gerard <jacquesg at pratique.fr>*Date*: Thu, 9 Oct 1997 01:42:40 -0400*Sender*: owner-wri-mathgroup at wolfram.com

Dear Patrick, When you ask Mathematica to calculate 0 Log[0] it has an indeterminacy (O by -Infinity) it cannot resolve because the elements of the product were calculated independently. If you ask for a Limit, like: Limit[ x Log[x], x->0] you have the result you expected: 0 In general you will have this limit for most classical functions going to 0 at 0 and typically any reasonable sum of (non 0) finite power of x. This is why one sometimes assume that 0 Log[0] is 0. But you must know how you are leading to 0. Olivier PS: Your question has allowed me to see that Mathematica (2.2 or 3.0.1) refuse to evaluate Limit[ x Log[ Exp[x^r] -1], x->0] if r is any fraction strictly superior to 2. My own calculation shows that the limit is still 0 and a plot of this function clearly supports this result. Perhaps people at WRI could explain this choice ? (the Standard Add-On Calculus`Limit` gives 0 in this case, putting a SeriesData::slnc error message meanwhile) At 06:05 +0200 97.10.08, Patrick Tao wrote: > Hello mma users, > > I have a quick question on the following computation: > > the natural log of 0 times 0 writen Log[0]*0 > > > > Should that not be 0 ? > > mma is returning an Indeterminate result > > Can somebody please help me understand this computation. > > > > Many Thanks > > -patrick