Symbols:R

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The Set of Real Numbers

$\R$

The set of real numbers.

The $\LaTeX$ code for $\R$ is \R  or \mathbb R or \Bbb 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

$\R_{\ne 0}$

The set of non-zero real numbers:

$\R_{\ne 0} = \R \setminus \left\{{0}\right\}$

The $\LaTeX$ code for $\R_{\ne 0}$ is \R_{\ne 0}  or \mathbb R_{\ne 0} or \Bbb R_{\ne 0}.

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

Deprecated

$\R^*$

The set of non-zero real numbers:

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

The $\LaTeX$ code for $\R^*$ is \R^*  or \mathbb R^* or \Bbb R^*.

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

The Set of Non-Negative Real Numbers

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

The $\LaTeX$ code for $\R_{\ge 0}$ is \R_{\ge 0}  or \mathbb R_{\ge 0} or \Bbb R_{\ge 0}.

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

Deprecated

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

The $\LaTeX$ code for $\R_+$ is \R_+  or \mathbb R_+ or \Bbb R_+.

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

The Set of Strictly Positive Real Numbers

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

The $\LaTeX$ code for $\R_{> 0}$ is \R_{> 0}  or \mathbb R_{> 0} or \Bbb R_{> 0}.

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

Deprecated

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

The $\LaTeX$ code for $\R_+^*$ is \R_+^*  or \mathbb R_+^* or \Bbb R_+^*.

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

The Set of Extended Real Numbers

$\overline \R$
$\overline \R = \R \cup \left\{{+\infty, -\infty}\right\}$

The $\LaTeX$ code for $\overline \R$ is \overline \R .

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

Real Part

$\Re \left({z}\right)$ or $\operatorname{Re} \left({z}\right)$

The real part of a complex number $z$.

The $\LaTeX$ code for $\Re \left({z}\right)$ is \Re \left({z}\right) .

The $\LaTeX$ code for $\operatorname{Re} \left({z}\right)$ is \operatorname{Re} \left({z}\right) .

Variants

Variants of $\operatorname{Re} \left({z}\right)$ and $\Re \left({z}\right)$ that can often be found are:

$\operatorname{\mathscr R} \left({z}\right)$
$\operatorname{re} \left({z}\right)$

The $\LaTeX$ code for $\operatorname{\mathscr R} \left({z}\right)$ is \operatorname{\mathscr R} \left({z}\right) .

The $\LaTeX$ code for $\operatorname{re} \left({z}\right)$ is \operatorname{re} \left({z}\right) .