$\mathbb{R}^\ast$, $\mathbb{R}_+$, $\mathbb{R}^\ast_+$ "deprecated"? I have recently stumbled upon this page in ProofWiki, which asserts that the notations
$$
\mathbb{R}^\ast = \mathbb{R}\setminus \{0\}
$$
and
$$
\mathbb{R}_+ = \{x\in\mathbb{R} \mid x\geq 0\}
$$
are both "deprecated." Is there a reason for that? (these notations are the ones I'm familiar with, and the ones I learnt since middle school)

If they're deprecated, they're deprecated for ProofWiki, certainly not in general.  Any particular forum or journal is free to choose their own standards for mathematical notation.  The main criterion should be to avoid confusion.  The problem with $\mathbb R_+$, I think, is that it may not be obvious whether you mean $\ge 0$ or $> 0$.  As for $\mathbb R^*$, perhaps it's that $^\star$ has many different meanings in different contexts.
