# Symbols:C

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### centi-

$\mathrm c$

The Système Internationale d'Unités symbol for the metric scaling prefix centi, denoting $10^{\, -2 }$, is $\mathrm { c }$.

Its $\LaTeX$ code is \mathrm {c} .

### Speed of Light

$c$

The speed of light (in a vacuum) is a physical constant.

Information cannot travel faster.

It is usually denoted $c$, and its value is given as:

$c = 299 \, 792 \, 458 \text { m s}^{-1}$

exactly.

The metre is in fact defined in terms of the speed of light and the definition of the second.

Its $\LaTeX$ code is c .

$\mathrm C$ or $\mathrm c$

The hexadecimal digit $12$.

Its $\LaTeX$ code is \mathrm C  or \mathrm c.

### Roman Numeral

$\mathrm C$ or $\mathrm c$

The Roman numeral for $100$.

Its $\LaTeX$ code is \mathrm C  or \mathrm c.

### Coulomb

$\mathrm C$

The symbol for the coulomb is $\mathrm C$.

Its $\LaTeX$ code is \mathrm C .

### Continuously Differentiable

$C^k$ or $\mathrm C^{\paren k}$

Let $f: \R \to \R$ be a real function.

Then $\map f x$ is of differentiability class $C^k$ if and only if:

$\dfrac {\d^k} {\d x^k} \map f x \in C$

where $C$ denotes the class of continuous real functions.

That is, $f$ is in differentiability class $k$ if and only if there exists a $k$th derivative of $f$ which is continuous.

The $\LaTeX$ code for $C^k$ is C^k .

The $\LaTeX$ code for $\mathrm C^{\paren k}$ is \mathrm C^{\paren k} .

### Smooth Real Function

$C^\infty$ or $\mathrm C^\omega$

A real function is smooth if and only if it is of differentiability class $C^\infty$.

That is, if and only if it admits of continuous derivatives of all orders.

The $\LaTeX$ code for $C^\infty$ is C^\infty .

The $\LaTeX$ code for $\mathrm C^\omega$ is \mathrm C^\omega .

### Set of Complex Numbers

$\C$

The set of complex numbers.

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

### Set of Non-Zero Complex Numbers

$\C_{\ne 0}$
$\C_{\ne 0} = \C \setminus \set 0$

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

### Extended Complex Plane

$\overline \C$

The extended complex plane $\overline \C$ is defined as:

$\overline \C := \C \cup \set \infty$

that is, the set of complex numbers together with the point at infinity.

The $\LaTeX$ code for $\overline \C$ is \overline \C  or \overline {\mathbb C} or \overline {\Bbb C}.

### Relative Complement

$\relcomp S T$ or $\map {\CC_S} T$

Let $S$ be a set, and let $T \subseteq S$, that is: let $T$ be a subset of $S$.

Then the set difference $S \setminus T$ can be written $\relcomp S T$, and is called the relative complement of $T$ in $S$, or the complement of $T$ relative to $S$.

Thus:

$\relcomp S T = \set {x \in S : x \notin T}$

The $\LaTeX$ code for $\relcomp S T$ is \relcomp S T .

The $\LaTeX$ code for $\map {\CC_S} T$ is \map {\CC_S} T .

### Set Complement

$\map \complement S$ or $\map \CC S$

The set complement (or, when the context is established, just complement) of a set $S$ in a universe $\mathbb U$ is defined as:

$\map \complement S = \relcomp {\mathbb U} S = \mathbb U \setminus S$

See the definition of Relative Complement for the definition of $\relcomp {\mathbb U} S$.

The $\LaTeX$ code for $\map \complement S$ is \map \complement S .

The $\LaTeX$ code for $\map \CC S$ is \map \CC S .

### cosh

$\cosh$

Its $\LaTeX$ code is \cosh .

### ch

$\operatorname {ch}$

A variant of $\cosh$.

Its $\LaTeX$ code is \operatorname {ch} .

### cosh${}^{-1}$

$\cosh^{-1}$

Its $\LaTeX$ code is \cosh^{-1} .

### ch${}^{-1}$

$\operatorname {ch}^{-1}$

A variant of $\cosh^{-1}$.

Its $\LaTeX$ code is \operatorname {ch}^{-1} .

### Centimetre

$\mathrm {cm}$

The symbol for the centimetre is $\mathrm {cm}$:

$\mathrm c$ for centi
$\mathrm m$ for metre.

Its $\LaTeX$ code is \mathrm {cm} .

### Candela

$\mathrm {cd}$

The symbol for the candela is $\mathrm {cd}$.

Its $\LaTeX$ code is \mathrm {cd} .

### Capacitance

$C$

The usual symbol used to denote capacitance is $C$.

Its $\LaTeX$ code is C .

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