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Does that mean that $x_1$ is all real numbers and $x_2$ is restricted to only positive numbers?

Jaideep Khare
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jian
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  • You sure whether it's $\Bbb{R_{++}}$ or $\Bbb{R^+}$? – Jaideep Khare Feb 04 '18 at 02:31
  • It's $R_{++}$. From what I understand they're the same thing, but $R^+$ is more ambiguous on whether it means non negative or strictly positive, where as $R_{++}$ means strictly positive and $R_+$ means non negative. – jian Feb 04 '18 at 02:40
  • I think this thread will avoid any confusion for future visitors of this question. – Jaideep Khare Feb 04 '18 at 02:44

1 Answers1

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Normally, $\mathbb{R}_+$ and $\mathbb{R}^+$ denote the set of positive reals. so you are correct, $f$ on $\mathbb{R} \times \mathbb{R}^+$ means the first variable is a real number and the second -- a positive real number.

gt6989b
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  • Oh I see. Thanks! – jian Feb 04 '18 at 02:26
  • $\mathbb{R}{+} = {x\in\mathbb{R} | x \geq 0$ while $\mathbb{R}{++} = {x\in\mathbb{R} | x \geq 0$. Thus it means $x_1$ is any real number and $x_2$ is any (strictly) positive real number. – max_zorn Feb 04 '18 at 02:29