Re: wierd Log[0] *0 result

• To: mathgroup at smc.vnet.net
• Subject: [mg9106] Re: [mg9022] wierd Log[0] *0 result
• From: ags at seaman.cc.purdue.edu (Dave Seaman)
• Date: Mon, 13 Oct 1997 23:33:20 -0400
• Organization: Purdue University
• Sender: owner-wri-mathgroup at wolfram.com

```In article <61k19o\$96u\$1 at dragonfly.wolfram.com>,
<seanross at worldnet.att.net> wrote:
>Patrick Tao wrote:

>> the natural log of 0 times 0 writen Log[0]*0
>>
>> Should that not be 0 ?
>>
>> mma is returning an Indeterminate result

>Log[0]=-Infinity
>
>Infinity * 0 is one of the seven standard indeterminate forms along
>with:
>
>0/0, Infinity/Infinity, 1^Infinity,  Infinity-Infinity, Infinity^0,
>zero^zero.
>
>I recommend a good pre-calc text as a brush up on limits.

I think both of you need to examine the difference between

0 Log[0]

and

Limit[x Log[x],x->0]

which are two different Mathematica expressions, representing two
entirely different concepts, and therefore it is not surprising that
they give entirely different results.  The first evaluates to
"Indeterminate", while the second evaluates to 0.

On the other hand, consider the expressions

Sign[0]

and

Limit[Sign[x],x->0]

where it turns out that the first expression is perfectly well defined,
but the second does not exist.

Conclusion:  you can't deduce anything about the value of a non-limit
expression by looking at a corresponding limit expression, or
conversely.

--
Dave Seaman			dseaman at purdue.edu
++++ stop the execution of Mumia Abu-Jamal ++++
++++ if you agree copy these lines to your sig ++++
++++ see http://www.xs4all.nl/~tank/spg-l/sigaction.htm ++++

```

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