Symbols:Analysis

Symbols used in Analysis

Norm

$\norm z$

Let $\struct {R, +, \circ}$ be a division ring with norm $\norm {\,\cdot\,}_R$.

Let $V$ be a vector space over $R$, with zero $0_V$.

A norm on $V$ is a map from $V$ to the nonnegative reals:

$\norm{\,\cdot\,}: V \to \R_{\ge 0}$

satisfying the (vector space) norm axioms:

\((\text N 1)\)	$:$		Positive Definiteness:	\(\ds \forall x \in V:\)		\(\ds \norm x = 0 \)	\(\ds \iff \)	\(\ds x = \mathbf 0_V \)
\((\text N 2)\)	$:$		Positive Homogeneity:	\(\ds \forall x \in V, \lambda \in R:\)		\(\ds \norm {\lambda x} \)	\(\ds = \)	\(\ds \norm {\lambda}_R \times \norm x \)
\((\text N 3)\)	$:$		Triangle Inequality:	\(\ds \forall x, y \in V:\)		\(\ds \norm {x + y} \)	\(\ds \le \)	\(\ds \norm x + \norm y \)

The $\LaTeX$ code for \(\norm z\) is \norm z .

Limit

$x \to 0$

$x \to a$

$x \to \infty$

Used to denote the statement that $a$ tends to the limit $0$, $a$ or $\infty$.

The $\LaTeX$ code for \(x \to 0\) is x \to 0 .

The $\LaTeX$ code for \(x \to a\) is x \to a .

The $\LaTeX$ code for \(x \to \infty\) is x \to \infty .

Asymptotic Equality

$\map f x \sim \map g x$

Denotes that $\map f x$ is asymptotically equal to $\map g x$.

The $\LaTeX$ code for \(\map f x \sim \map g x\) is \map f x \sim \map g x .

Integral Sign

$\ds \int$

The integral sign.

The $\LaTeX$ code for \(\ds \int\) is \ds \int .

Multiple Integral

$\ds \iint$

$\ds \iiint$

$\ds \iiiint$

$\ds \idotsint$

The multiple integral sign.

The $\LaTeX$ code for \(\ds \iint\) is \ds \iint .

The $\LaTeX$ code for \(\ds \iiint\) is \ds \iiint .

The $\LaTeX$ code for \(\ds \iiiint\) is \ds \iiiint .

The $\LaTeX$ code for \(\ds \idotsint\) is \ds \idotsint .