Take the 2-minute tour ×
Mathematica Stack Exchange is a question and answer site for users of Mathematica. It's 100% free, no registration required.

Let's say that $x$ is some real valued number $>0$.
Are the following commands interchangeable in the context of using Assuming?

  1. Assuming[{Re[x] > 0}, Integrate[...,x]]
  2. Assuming[{x ∈ Reals && x > 0}, Integrate[...,x]]

Or, as I suspect, is this not true for the reason that Re[x] > 0 should just mean that the Real component of $x$ is $>0$? Also, is there a way to more compactly specify {x ∈ Reals && x > 0}?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

No. Re[x] > 0 means that the real part of x is positive, but it does not mean that the imaginary part is zero. Re[1+I] > 0 but 1+I is not real.

However, x > 0 is sufficient and (in Mathematica) implies that x is also real.

share|improve this answer
Thanks, I just saw some strange behavior for ConditionalExpression and it made me wonder, so I'll think more carefully about my integral. I'll accept your answer after the timer allows me to. –  user11959 Jan 26 at 1:15
"However, x > 0 is sufficient and (in Mathematica) implies that x is also real." Hmm, I'm wondering if this is a little dangerous? –  user11959 Jan 26 at 1:16
@user11959 How is it dangerous? –  Mr.Wizard Jan 26 at 1:18
@user11959 Not Norm, but Abs, in this case. The idea is that comparisons don't make sense for complex number. As soon as you use a comparison, Mathematica assumed that the associated variable is real. Yes, this is a peculiarity of Mathematica that you need to be aware of and not something immediately obvious. –  Szabolcs Jan 26 at 1:24
@Szabolcs I can see why it makes sense, but I'm glad to have been explicitly told about it all the same, thanks for that. –  user11959 Jan 26 at 1:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.