Symbols:Z

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 $Y$.

Set of Integers

 * $\Z$

The set of integers:
 * $\Z = \set {\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}$.

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

Set of Non-Zero Integers

 * $\Z_{\ne 0}$

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

Deprecated

 * $\Z^*$

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

Set of Non-Negative Integers

 * $\Z_{\ge 0}$

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

Deprecated

 * $\Z_+$

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

Set of Strictly Positive Integers

 * $\Z_{> 0}$

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

Deprecated

 * $\Z_+^*$

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

Reduced Residue System Modulo $m$

 * $\Z'_m$

Set of Integer Multiples

 * $n \Z$

The Set of Integer Multiples $n \Z$ is defined as:
 * $\set {x \in \Z: n \divides x}$

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

 * $\Z \sqbrk i$

Subsets of Integers

 * $\map \Z n$

Used by some authors to denote the set of all integers between $1$ and $n$ inclusive:
 * $\map \Z n = \set {x \in \Z: 1 \le x \le n} = \set {1, 2, \ldots, n}$

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