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 .


Hexadecimal

$\mathrm C$ 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

$\C_{\ne 0}$

The set of non-zero complex numbers:

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


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 .


Hyperbolic Cosine

cosh

$\cosh$

Hyperbolic cosine.


Its $\LaTeX$ code is \cosh .


ch

$\operatorname {ch}$

Hyperbolic cosine.

A variant of $\cosh$.


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


Inverse Hyperbolic Cosine

cosh${}^{-1}$

$\cosh^{-1}$

Inverse hyperbolic cosine.


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


ch${}^{-1}$

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

Inverse hyperbolic cosine.

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} .


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