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I know that both of them contain all positive numbers from $\mathbb{R}$ but one notation contains $0$ too. I don't know which one.

Thanks in advance.

Ge To
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    See https://en.wikipedia.org/wiki/Positive_real_numbers for the different existing notations. – TheSilverDoe Feb 18 '21 at 09:05
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    $\mathbb{R}^$ and $\mathbb{Q}^$ and $\mathbb{Z}^*$ might typically be the whole set excluding $0$ but keeping negative values – Henry Feb 18 '21 at 09:20

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$\Bbb R^+ = \{r\in \Bbb R\mid r>0\}$ (open half space) and $\Bbb R^* = \Bbb R\setminus\{0\}$ (carrier set of multiplicative group of field $\Bbb R$).

Wuestenfux
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    Be careful, it depends on convention/languages : $\mathbb{R}^+$ sometimes stands for $\lbrace r \in \mathbb{R}, r\geq 0 \rbrace$, in which case we write $\mathbb{R}_+^*$ for $\lbrace r \in \mathbb{R}, r > 0 \rbrace$. – TheSilverDoe Feb 18 '21 at 09:01
  • @TheSilverDoe yes indeed, in fact I recall writing $\mathbb{R}^{+*}$ in highschool in France 40 years ago. – user3733558 Feb 18 '21 at 09:07
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    @user3733558 ... and this notation is still used today in France :) – TheSilverDoe Feb 18 '21 at 09:08