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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