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. > > ADL > > <snipped/>