Symbols:S
Second
- $\mathrm s$
The symbol for the second is $\mathrm s$.
Its $\LaTeX$ code is \mathrm s .
Set
- $S$
Used to denote a general set.
The $\LaTeX$ code for \(S\) is S .
Algebraic Structure
- $S$
Used to denote a general algebraic structure, in particular a semigroup.
In this context, frequently seen in the compound symbol $\struct {S, \circ}$ where $\circ$ represents an arbitrary binary operation.
The $\LaTeX$ code for \(\struct {S, \circ}\) is \struct {S, \circ} .
South
- $\mathrm S$
South is the direction on (or near) Earth's surface along the meridian directly towards the South Pole.
The $\LaTeX$ code for \(\mathrm S\) is \mathrm S .
Southeast
- $\mathrm {SE}$
Southeast is the direction on (or near) Earth's surface halfway between south and east.
The $\LaTeX$ code for \(\mathrm {SE}\) is \mathrm {SE} .
Southwest
- $\mathrm {SW}$
Southwest is the direction on (or near) Earth's surface halfway between south and west.
The $\LaTeX$ code for \(\mathrm {SW}\) is \mathrm {SW} .
Set of Permutations
- $S_n$
The set of permutations of $\N_n$ is denoted $S_n$.
The $\LaTeX$ code for \(S_n\) is S_n .
Symmetric Group
- $\struct {S_n, \circ}$
Let $S_n$ denote the set of permutations on $n$ letters.
Let $\struct {S_n, \circ}$ denote the symmetric group on $S_n$.
Then $\struct {S_n, \circ}$ is referred to as the symmetric group on $n$ letters.
The $\LaTeX$ code for \(\struct {S_n, \circ}\) is \struct {S_n, \circ} .
Signum Function
- $\map \sgn x$
Let $X \subseteq \R$ be a subset of the real numbers.
The signum function $\sgn: X \to \set {-1, 0, 1}$ is defined as:
- $\forall x \in X: \map \sgn x := \sqbrk {x > 0} - \sqbrk {x < 0}$
where $\sqbrk {x > 0}$ etc. denotes Iverson's convention.
That is:
- $\forall x \in X: \map \sgn x := \begin{cases} -1 & : x < 0 \\ 0 & : x = 0 \\ 1 & : x > 0 \end{cases}$
The $\LaTeX$ code for \(\map \sgn x\) is \map \sgn x .
Filtering Function
- $\map {\operatorname {sinc} } x$
The filtering function is the real function $\operatorname {sinc}: \R \to \R$ defined as:
- $\forall x \in \R: \map {\operatorname {sinc} } x := \dfrac {\sin \pi x} {\pi x}$
where $\sin$ denotes the (real) sine function.
The $\LaTeX$ code for \(\map {\operatorname {sinc} } x\) is \map {\operatorname {sinc} } x .