Symbols:Z

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zepto-

$\mathrm z$

The Système Internationale d'Unités metric scaling prefix denoting $10^{\, -21 }$.


Its $\LaTeX$ code is \mathrm {z} .


zetta-

$\mathrm Z$

The Système Internationale d'Unités metric scaling prefix denoting $10^{\, 21 }$.


Its $\LaTeX$ code is \mathrm {Z} .


General Variable

$z$

Used to denote a general variable, usually in conjunction with other variables $x$ and $y$.


Complex Variable

Used to denote a general variable in the complex plane.


The $\LaTeX$ code for \(z\) is z .


Random Variable

$Z$

Used to denote a general random variable, usually in conjunction with another random variables $X$ and $Y$.


The $\LaTeX$ code for \(Z\) is Z .


The Set of Integers

$\Z$

The set of integers:

$\Z = \left\{{\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}\right\}$.

From the German Zahlen, which means (whole) numbers.


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


The Set of Non-Zero Integers

$\Z_{\ne 0}$

The set of non-zero integers:

$\Z_{\ne 0} = \Z \setminus \left\{{0}\right\} = \left\{{\ldots, -3, -2, -1, 1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z_{\ne 0}\) is \Z_{\ne 0} .


Deprecated

$\Z^*$

The set of non-zero integers:

$\Z^* = \Z \setminus \left\{{0}\right\} = \left\{{\ldots, -3, -2, -1, 1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z^*\) is \Z^* .


The Set of Non-Negative Integers

$\Z_{\ge 0}$

The set of non-negative integers:

$\Z_{\ge 0} = \left\{{n \in \Z: n \ge 0}\right\} = \left\{{0, 1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z_{\ge 0}\) is \Z_{\ge 0}  or \mathbb Z_{\ge 0}.


Deprecated

$\Z_+$

The set of non-negative integers:

$\Z_+ = \left\{{n \in \Z: n \ge 0}\right\} = \left\{{0, 1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z_+\) is \Z_+  or \mathbb Z_+.


The Set of Strictly Positive Integers

$\Z_{> 0}$

The set of strictly positive integers:

$\Z_{> 0} = \left\{{n \in \Z: n > 0}\right\} = \left\{{1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z_{> 0}\) is \Z_{> 0}  or \mathbb Z_{> 0} or \Bbb Z_{> 0}.


Deprecated

$\Z_+^*$

The set of strictly positive integers:

$\Z_+^* = \left\{{n \in \Z: n > 0}\right\} = \left\{{1, 2, 3, \ldots}\right\}$


The $\LaTeX$ code for \(\Z_+^*\) is \Z_+^*  or \mathbb Z_+^* or \Bbb Z_+^*.


Reduced Residue System Modulo $m$

$\Z'_m$


The reduced residue system modulo $m$, denoted $\Z'_m$, is the set of all residue classes of $k$ (modulo $m$) which are prime to $m$:

$\Z'_m = \set {\eqclass k m \in \Z_m: k \perp m}$


Thus $\Z'_m$ is the set of all coprime residue classes modulo $m$:

$\Z'_m = \set {\eqclass {a_1} m, \eqclass {a_2} m, \ldots, \eqclass {a_{\map \phi m} } m}$

where:

$\forall k: a_k \perp m$
$\map \phi m$ denotes the Euler phi function of $m$.


The $\LaTeX$ code for \(\Z'_m\) is \Z'_m  or \mathbb Z'_m or \Bbb Z'_m.


The Set of Integer Multiples

$n \Z$

The Set of Integer Multiples $n \Z$ is defined as:

$\left\{ {x \in \Z: n \mathrel \backslash x}\right\}$

for some $n \in \N$.

That is, it is the set of all integers which are divisible by $n$, that is, all multiples of $n$.


The $\LaTeX$ code for \(n \Z\) is n \Z .


The Gaussian Integers

$\Z \left[{i}\right]$

A Gaussian integer is a complex number whose real and imaginary parts are both integers.

That is, a Gaussian integer is a number in the form:

$a + b i: a, b \in \Z$


The set of all Gaussian integers can be denoted $\Z \left[{i}\right]$, and hence can be defined as:

$\Z \left[{i}\right] = \left\{{a + b i: a, b \in \Z}\right\}$


The $\LaTeX$ code for \(\Z \left[{i}\right]\) is \Z \left[{i}\right] .


Subsets of Integers

$\Z \left({n}\right)$

Used by some authors to denote the set of all integers between $1$ and $n$ inclusive:

$\Z \left({n}\right) = \left\{{x \in \Z: 1 \le x \le n}\right\} = \left\{{1, 2, \ldots, n}\right\}$

That is, an alternative to Initial Segment of Natural Numbers $\N^*_n$.


The $\LaTeX$ code for \(\Z \left({n}\right)\) is \Z \left({n}\right) .