Symbol for set of strictly positive real numbers? Is there any standard symbol for the set $\{x\in\mathbb{R} : x > 0\}$?
I think $\mathbb{R}^{+}$ usually includes zero. Some sources say I should use $\mathbb{R}^{*}_{+}$ but it looks slightly bizarre to me.
Suggestions?
 A: $\mathbb{R}_{\ge a}$ is VERY standard for $[a,+\infty)\subset\mathbb{R}$ and $\mathbb{R}_{> a}$ for $(a,+\infty)\subset\mathbb{R}$
This is a very obvious "There is no other sensible interpretation" convetion, if I give you $\mathbb{R}_{\le -5}$ you know immediately I mean $(-\infty,-5]$
I have seen $\mathbb{R}^+$ used - this follows the $\mathbb{N}^+=\{1,2,\cdots\}$ convention but I don't like this because it isn't as obvious.
Oh to answer your question, strictly positive reals: $$\mathbb{R}_{>0}=(0,\infty)=\{x\in\mathbb{R}|x>0\}$$
A: There is no one single universal standard symbol recognised and used by everyone. Something like $\mathbb{R}^{>0}$ or $\mathbb{R}_{>0}$ is clear enough (I have seen people use both); $\mathbb{R}^*_+$ makes sense but I've never seen anyone use it.
A: Well, why don't you give $(0,+\infty)$ a chance? Anyway, positive numbers are different from non-negative numbers: therefore I'd guess that $\mathbb{R}^{+} = \{ x \in \mathbb{R} \mid x>0\}$, and $\{ x \in \mathbb{R} \mid x \geq 0\} = \mathbb{R}^{+} \cup \{0\}$.
But many people prefer to include zero for mere convenience, so that it is improbable to reach a universal agreement.
