       Re: no message from Minimize[] on a weird function(x^x) !?!

• To: mathgroup at smc.vnet.net
• Subject: [mg96800] Re: no message from Minimize[] on a weird function(x^x) !?!
• From: congruentialuminaire at yahoo.com
• Date: Wed, 25 Feb 2009 04:03:56 -0500 (EST)
• References: <gnr1d2\$ep0\$1@smc.vnet.net> <go0j9l\$n5r\$1@smc.vnet.net>

```Thanks MathGroup for so much good info about this.

I knew that this function is ill-behaved when x < 0. I have some other
functions which are not so "simple" as x^x. I use Minimize[] first
rather than the numerical invocations since it knows how to handle an
equation with parameters.

I guess I want it to issue some message when it can't perform what I
ask. I will start reading the "Possible Issues" when I run into
problems.

Regards..RogerW

On Feb 24, 2:48 am, ADL <alberto.dilu... at tiscali.it> wrote:
> Beyond what others have already commented, I would say that the
> problem stems with the definition of 0^0 which, in Mathematica, is
> Indeterminate. In fact, even if the value of the function is
> constrained to be real positive, Minimize behavior is influenced by
> the value at 0:
>
> Minimize[{Abs[x^x], x > 0}, x] // InputForm
> {E^(-E^(-1)), {x -> E^(-1)}}
>
> Minimize[{Abs[x^x], x < 0}, x] // InputForm
> {0, {x -> -Infinity}}
>
> Minimize[{Abs[x^x], x >= 0}, x] // InputForm
> Minimize[{Abs[x^x], x >= 0}, x]
>
> In fact,
>
> 0^0
> Indeterminate
>
> but
> Limit[Abs[x^x], x -> 0]
> 1.
>
> In conclusion, Minimize does not appear to compute limits and cannot
> deal with "holes" in the function's domain.
>