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 .


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 (Set 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 and third quartiles.

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 real function $\operatorname {III}: \R \to \R$ defined as:

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

where $\delta$ denotes the Dirac delta function.


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