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should Positive[ complexNumber ] return undefined instead of False?

• To: mathgroup at smc.vnet.net
• Subject: [mg112582] should Positive[ complexNumber ] return undefined instead of False?
• From: "Nasser M. Abbasi" <nma at 12000.org>
• Date: Tue, 21 Sep 2010 02:04:18 -0400 (EDT)
• Reply-to: nma at 12000.org

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?

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?

--Nasser

• Follow-Ups:
  • Re: should Positive[ complexNumber ] return undefined instead of False?
    • From: Andrzej Kozlowski <akoz@mimuw.edu.pl>