# Symbols:R

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### Set of Real Numbers

$\R$

The set of real numbers.

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

### Set of Non-Zero Real Numbers

$\R_{\ne 0}$

The set of non-zero real numbers:

$\R_{\ne 0} = \R \setminus \set 0$

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

### Set of Non-Negative Real Numbers

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

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

### Set of Strictly Positive Real Numbers

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

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

### Extended Real Number Line

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

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

### Real Euclidean Space

$\R^n$

Let $\R^n$ be an $n$-dimensional real vector space.

Let the Euclidean metric $d$ be applied to $\R^n$.

Then $\struct {\R^n, d}$ is a Euclidean $n$-space.

The $\LaTeX$ code for $\R^n$ is \R^n .

The $\LaTeX$ code for $\struct {\R^n, d}$ is \struct {\R^n, d} .

### Real Part

$\map \Re z$ or $\map {\operatorname {Re} } z$

The real part of a complex number $z$.

The $\LaTeX$ code for $\map \Re z$ is \map \Re z .

The $\LaTeX$ code for $\map {\operatorname {Re} } z$ is \map {\operatorname {Re} } z .