Re: should Positive[ complexNumber ] return undefined instead of False?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112631] Re: should Positive[ complexNumber ] return undefined instead of False?*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Thu, 23 Sep 2010 04:41:07 -0400 (EDT)*References*: <201009210604.CAA25100@smc.vnet.net>

On 21 Sep 2010, at 08:04, Nasser M. Abbasi wrote: > > math experts: > > x = 3*I; > Positive[x] > > Out[59]= False > > Should this be undefined or unevaluated? > > If it is False, when there must be an case when it is True, right? but > there is not such case, positive and negative are not defined on the > complex numbers, or Am I missing something? Note that Through[{Positive, Negative}[I]] {False,False} In other words, I is neither positive nor negative. > > I know the above works as documented: > > "Positive[x] gives False if x is manifestly a negative numerical > quantity, a complex numerical quantity, or zero. Otherwise, it remains > unevaluated" > > So, my question is just wanting to know why when Mathematica was > designed, the complexes were not added to the case where they remains > unevaluated in this case? Well, I think the "philosophy" is to return an expression of the form Positive[x] unevaluated so that it can later return a value when x is assigned a value. I.e. Positive[x] /. x -> 2 True But obviously this makes no sense in this case of I since you can't = assign values to I and even: Unevaluated[Positive[I]] /. I -> 2 False So the answer, in my opinion, is that, wether logically justified or = not, returning Positive[I] unevaluated would have no practical use = hence it is not done. Andrzej Kozlowski

**References**:**should Positive[ complexNumber ] return undefined instead of False?***From:*"Nasser M. Abbasi" <nma@12000.org>