# Symbols:I

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### Roman Numeral

$\mathrm I$ or $\mathrm i$

The Roman numeral for $1$.

Its $\LaTeX$ code is \mathrm I  or \mathrm i.

### Imaginary Unit

$i$

The entity $i := 0 + 1 i$ is known as the imaginary unit.

The $\LaTeX$ code for $i$ is i .

### Identity Element

$i$ or $I$

Used (rarely) to denote the identity element of a group $\struct {G, \circ}$:

$\forall x \in G: i \circ x = x = x \circ i$

The $\LaTeX$ code for $i$ is i .

The $\LaTeX$ code for $I$ is I .

### Unit $x$ Vector

$\mathbf i$

Used to denote the unit vector in the positive direction of the $x$-axis.

The $\LaTeX$ code for $\mathbf i$ is \mathbf i .

### Unit Quaternion

$\mathbf i$

Used to denote one of the units in the system of quaternions.

The $\LaTeX$ code for $\mathbf i$ is \mathbf i .

### Identity Matrix

$\mathbf I_n$

Used to denote the identity matrix whose order is $n$.

When the order is understood or not specified, the symbol $\mathbf I$ is used.

The $\LaTeX$ code for $\mathbf I_n$ is \mathbf I_n .

### Identity Mapping

$I_S$

Used to denote the identity mapping on a set $S$:

$\forall x \in S: \map {I_S} x = x$

When the set itself is understood, it is commonplace to leave out the subscript.

The $\LaTeX$ code for $\map {I_S} x$ is \map {I_S} x .

### Set of Integers

$\Bbb I$

Rarely used instead of $\Z$ for the set of integers:

$\Bbb I = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$.

Its $\LaTeX$ code is \Bbb I  or \mathbb I.

### Imaginary Part

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

The imaginary part of a complex number $z$.

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

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

### Image (Relation Theory)

$\operatorname {Img}$

Denotes the image of a relation or the image of a mapping.

The $\LaTeX$ code for $\Img {\RR}$ is \Img {\RR} .

### Interquartile Range

$\operatorname {IQR}$

Let $Q_1$ and $Q_3$ be first quartile and third quartile respectively.

The interquartile range is defined and denoted as:

$\operatorname {IQR} := Q_3 - Q_1$

The $\LaTeX$ code for $\operatorname {IQR}$ is \operatorname {IQR} .

### Even Impulse Pair Function

$\map {\operatorname {II} } x$

The even impulse pair function is the real function $\operatorname {II}: \R \to \R$ defined as:

$\forall x \in \R: \map {\operatorname {II} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} + \dfrac 1 2 \map \delta {x - \dfrac 1 2}$

where $\delta$ denotes the Dirac delta function.

The $\LaTeX$ code for $\map {\operatorname {II} } x$ is \map {\operatorname {II} } x .

### Odd Impulse Pair Function

$\map {\operatorname {I_I} } x$

The odd impulse pair function is the real function $\operatorname {I_I}: \R \to \R$ defined as:

$\forall x \in \R: \map {\operatorname {I_I} } x := \dfrac 1 2 \map \delta {x + \dfrac 1 2} - \dfrac 1 2 \map \delta {x - \dfrac 1 2}$

where $\delta$ denotes the Dirac delta function.

The $\LaTeX$ code for $\map {\operatorname {I_I} } x$ is \map {\operatorname {I_I} } x .

### Sampling Function

$\map {\operatorname {III} } x$

The sampling function is the distribution $\operatorname {III}_T: \map \DD \R \to \R$ defined as:

$\forall x \in \R: \map {\operatorname {III}_T } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - T n}$

where:

$T \in \R_{\ne 0}$ is a non-zero real number
$\delta$ denotes the Dirac delta distribution.

When $T = 1$, it is usually omitted:

$\forall x \in \R: \map {\operatorname {III} } x := \ds \sum_{n \mathop \in \Z} \map \delta {x - n}$

The $\LaTeX$ code for $\map {\operatorname {III} } x$ is \map {\operatorname {III} } x .

### Electric Current

$I$ or $i$

The usual symbols used to denote an electric current when only its scalar magnitude is being discussed is $I$ or $i$.

The $\LaTeX$ code for $I$ is I .

The $\LaTeX$ code for $i$ is i .

### Luminous Intensity

$I$

The usual symbol used to denote luminous intensity is $I$.

Its $\LaTeX$ code is I .

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