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.

Random Variable

 * $Z$

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

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 Set of Non-Zero Integers

 * $\Z_{\ne 0}$

The set of non-zero integers:
 * $\Z_{\ne 0} = \Z \setminus \left\{{0}\right\} = \left\{{\ldots, -3, -2, -1, 1, 2, 3, \ldots}\right\}$

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 Set of Non-Negative Integers

 * $\Z_{\ge 0}$

The set of non-negative integers:
 * $\Z_{\ge 0} = \left\{{n \in \Z: n \ge 0}\right\} = \left\{{0, 1, 2, 3, \ldots}\right\}$

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 Set of Strictly Positive Integers

 * $\Z_{> 0}$

The set of strictly positive integers:
 * $\Z_{> 0} = \left\{{n \in \Z: n > 0}\right\} = \left\{{1, 2, 3, \ldots}\right\}$

Deprecated

 * $\Z_+^*$

The set of strictly positive integers:
 * $\Z_+^* = \left\{{n \in \Z: n > 0}\right\} = \left\{{1, 2, 3, \ldots}\right\}$

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 Set of Integer Multiples

 * $n \Z$

The Set of Integer Multiples $n \Z$ is defined as:
 * $\left\{{x \in \Z: n \mathop \backslash x}\right\}$

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 Gaussian Integers

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

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 $\N^*_n$.