What does $\mathbb{R}_{++}$ stand for?

Question

What does $\mathbb{R}_{++}$ mean?

I know $\mathbb{R}_+$ means all non-negative real numbers, but I have no clue what $\mathbb{R}_{++}$ means.

I don't think it is standard notation. Where have you seen it? — hmakholm left over Monica, Sep 02 '12 at 20:24

score 16 · Answer 1 · answered Sep 02 '12 at 20:11

16

It usually means the set of all positive real numbers, $\mathbb{R}_{++} = (0,\infty)$. Of course, there might be more symbols for this set.

answered Sep 02 '12 at 20:11

Kartik Audhkhasi

2

Right, because $\mathbb{R}_{+}$ is ambiguous, as some authors use it for $[0,\infty)$ and some for $(0,\infty)$. – cyberSingularity Sep 02 '12 at 21:43
3

I have seen it used this way fairly often. – Michael Greinecker Sep 02 '12 at 21:45
3

--in economics books. – Michael Greinecker Sep 02 '12 at 21:54
But don't most math books use $\mathbb{R}^{+}$ instead? – Arbuja Apr 29 '17 at 22:37
1

Convex optimization also uses this notation. – FountainTree Jan 25 '23 at 23:18

score 7 · Answer 2 · edited Jan 31 '16 at 17:35

7

From my Course: Probabilistic Methods in Finance, we denoted $R+, R++$ like so: $$R+ =\{x\in R : x\ge0\}$$ $$R++ =\{x\in R : x≫0\}.$$

edited Jan 31 '16 at 17:35

Alekos Robotis

answered Jan 31 '16 at 17:14

jojo

3

What does $ x≫0 $ mean? Shouldn't it be $\mathbb{R}_{++} ={x\in \mathbb{R} : x>0}$. – john Aug 14 '17 at 02:36
@john (3 years late, but may still be useful) It means "much greater than" (it's not precise); see this question for the "much less than" counterpart. – Just_A_User Nov 16 '21 at 10:06

score 1 · Answer 3 · answered Sep 02 '12 at 21:42

Im not completely sure , but i believe it means strictly positive. Thus not the negative reals NOR zero.

Well assuming the context is real numbers that is.

I believe it is used in countries where R+ is meant to include 0. In most countries R+ does not include 0 , hence the extra symbol.

It might help to read over again to get an idea.

3 Answers3