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

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? Sep 2, 2012 at 20:24
• I would say: Look in the previous pages of that book. Sep 2, 2012 at 21:01
• Maybe it's a programming language... :-) Sep 2, 2012 at 21:46
• Since HELP never came back, maybe we can close this. Jan 31, 2016 at 17:53

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

• Right, because $\mathbb{R}_{+}$ is ambiguous, as some authors use it for $[0,\infty)$ and some for $(0,\infty)$. Sep 2, 2012 at 21:43
• I have seen it used this way fairly often. Sep 2, 2012 at 21:45
• --in economics books. Sep 2, 2012 at 21:54
• But don't most math books use $\mathbb{R}^{+}$ instead? Apr 29, 2017 at 22:37
• Convex optimization also uses this notation. Jan 25, 2023 at 23:18

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

• What does $x≫0$ mean? Shouldn't it be $\mathbb{R}_{++} =\{x\in \mathbb{R} : x>0\}$.
– john
Aug 14, 2017 at 2:36
• @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. Nov 16, 2021 at 10:06

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.