Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Can anyone tell me what $\mathbb R^2_{++}$ means? Is it different from $\mathbb R^2_+$?

Thank you so much!

Edit (answer): This is what the author meant (I found it in the lecture notes by the same professor but of a different course): $\mathbb R^2_{++}=\{(x,y)\in\mathbb R^2\mid x>0, y>0\}$ , while $\mathbb R^2_+=\{(x,y)\in\mathbb R^2\mid x≥0, y≥0\}$ .

share|cite|improve this question
Please confirm that I LaTeX'd your notation properly. – Asaf Karagila Dec 21 '12 at 11:56
yes, that's exactly what i meant. thank you – babbo natale Dec 21 '12 at 12:00
What do you think $\mathbb{R}^2_+$ means? (It's not entirely obvious.) My guess would be that $\mathbb{R}^2_{++}$ is supposed to denote $(\mathbb{R}_+)^2$, i.e. the set of points $(x,y)$ where both coordinates are positive, but check the text where you found it. There is probably a definition somewhere (at least, there should be). I have never seen this notation before. – mrf Dec 21 '12 at 12:03
@mrf: I've used that notation $\mathbb{R}^2_{++}$ previously (and privately only). It is somewhat useful in convex analysis when sometimes one has to consider individual orthants, and so $\mathbb{R}^n_{+++---+\cdots +}$ can be useful sometimes to keep track of the combinatorics. On the other hand, I don't ever use $\mathbb{R}^2_+$: if I want a half-space I call it $\mathbb{R}_+\times \mathbb{R}^n$. – Willie Wong Dec 21 '12 at 12:49
As a follow up: in 2D there is a usual convention for numbering the quadrants. (Though I often forget which is second and which is fourth.) But in higher dimensions I am not aware of any established numbering convention... – Willie Wong Dec 21 '12 at 12:50

This is not a usual notation, so it should probably be mentioned somewhere, but a reasonable guess would be $\{(x,y)\in\mathbb R^2\mid x>0, y>0\}$.

If you supply more context, and in particular where you have seen this notation perhaps further information can be given.

share|cite|improve this answer
It comes from an example of utility functions. – babbo natale Dec 21 '12 at 12:14
Again, more details on where you found that example will help. (Note that "in a book" or "online" is not a helpful expansion of current knowledge of the whereabouts of this example.) – Asaf Karagila Dec 21 '12 at 12:17
It comes from an example of utility functions. Let u:R^2_+ --> R such that u(x)=(a*(x_1)^b+(1-a)(x_2)^b)^(1/b) with a in [0,1] anb b in (0,1]. Let v:R^2_++ -->R such that v(x)=(x_1)^c*(x_2)^(1-c) with c in [0,1]. This example should show that this 2 utility functions have different domain. – babbo natale Dec 21 '12 at 12:20
I found it in some lecture notes, there is no way to ask directly to the professor who wrote it. – babbo natale Dec 21 '12 at 12:23
@babbonatale: Asaf's point is that "details about where you found that example" means tell us the author and title of the book, preferrably plus edition and page number. – Henning Makholm Dec 21 '12 at 12:25

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.