# What does the notation $\mathbb R^2_{++}$ mean?

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 $\mathbb R^2_+=\{(x,y)\in\mathbb R^2\mid x≥0, y≥0\}$ .

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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 $\{(x,y)\in\mathbb R^2\mid x>0, y>0\}$.