Symbols:R

The Set of Real Numbers

$\R$

The set of real numbers.

Its $\LaTeX$ code is \mathbb R or (preferably) \R.

MediaWiki $\LaTeX$ also allows \reals, but MathJax does not recognise that as a valid code.

Some authors use $R$.

The Set of Non-Zero Real Numbers

$\R^*$

The set of non-zero real numbers:

$\R^* = \R \setminus \left\{{0}\right\}$

Its $\LaTeX$ code is \mathbb R^* or (preferably) \R^*.

MediaWiki $\LaTeX$ also allows \reals^*, but MathJax does not recognise that as a valid code.

The Set of Non-Negative Real Numbers

$\R_{\ge 0}$

The set of non-negative real numbers:

$\R_{\ge 0} = \left\{{x \in \R: x \ge 0}\right\}$

Its $\LaTeX$ code is \mathbb R_{\ge 0} or (preferably) \R_{\ge 0}.

MediaWiki $\LaTeX$ also allows \reals_{\ge 0}, but MathJax does not recognise that as a valid code.

Deprecated

$\R_+$

The set of non-negative real numbers:

$\R_+ = \left\{{x \in \R: x \ge 0}\right\}$

Its $\LaTeX$ code is \mathbb R_+ or (preferably) \R_+.

MediaWiki $\LaTeX$ also allows \reals_+, but MathJax does not recognise that as a valid code.

The Set of Strictly Positive Real Numbers

$\R_{> 0}$

The set of strictly positive real numbers:

$\R_{> 0} = \left\{{x \in \R: x > 0}\right\}$

Its $\LaTeX$ code is \mathbb R_{> 0} or (preferably) \R_{> 0}.

MediaWiki $\LaTeX$ also allows \reals_{> 0}, but MathJax does not recognise that as a valid code.

Deprecated

$\R_+^*$

The set of strictly positive real numbers:

$\R_+^* = \left\{{x \in \R: x > 0}\right\}$

Its $\LaTeX$ code is \mathbb R_+^* or (preferably) \R_+^*.

MediaWiki $\LaTeX$ also allows \reals_+^*, but MathJax does not recognise that as a valid code.