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

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

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    $\begingroup$ I don't think it is standard notation. Where have you seen it? $\endgroup$ Sep 2, 2012 at 20:24
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    $\begingroup$ I would say: Look in the previous pages of that book. $\endgroup$
    – GEdgar
    Sep 2, 2012 at 21:01
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    $\begingroup$ Maybe it's a programming language... :-) $\endgroup$
    – Asaf Karagila
    Sep 2, 2012 at 21:46
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    $\begingroup$ Since HELP never came back, maybe we can close this. $\endgroup$
    – GEdgar
    Jan 31, 2016 at 17:53

3 Answers 3

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

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    $\begingroup$ Right, because $\mathbb{R}_{+}$ is ambiguous, as some authors use it for $[0,\infty)$ and some for $(0,\infty)$. $\endgroup$ Sep 2, 2012 at 21:43
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    $\begingroup$ I have seen it used this way fairly often. $\endgroup$ Sep 2, 2012 at 21:45
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    $\begingroup$ --in economics books. $\endgroup$ Sep 2, 2012 at 21:54
  • $\begingroup$ But don't most math books use $\mathbb{R}^{+}$ instead? $\endgroup$
    – Arbuja
    Apr 29, 2017 at 22:37
  • $\begingroup$ Convex optimization also uses this notation. $\endgroup$ Jan 25, 2023 at 23:18
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From my Course: Probabilistic Methods in Finance, we denoted $R+, R++$ like so: $$R+ =\{x\in R : x\ge0\}$$ $$R++ =\{x\in R : x≫0\}.$$

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

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