Symbols: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.

The $\LaTeX$ code for $\Z$ is \Z.

The Set of Non-Zero Integers

$\Z^*$

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 \mathbb Z_{\ge 0} or \Z_{\ge 0}.

Deprecated

$\Z_+$

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 $\Z_+$ is \mathbb Z_+ or \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 \mathbb Z_{> 0} or \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 \mathbb Z_+^* or \Z_+^*.

The Set of Coprime Integers Modulo m

$\Z'_m$

The set $\Z'_m$ is the set of all integers modulo $m$ which are prime to $m$:

$\Z'_m = \left\{{\left[\!\left[{k}\right]\!\right]_m \in \Z_m: k \perp m}\right\}$.

See Set of Coprime Integers.

The $\LaTeX$ code for $\Z'_m$ is \Z'_m.

The Set of Integer Multiples

$n \Z$

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

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

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 Subsets of Natural Numbers $\N^*_n$.

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