Symbols: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 \mathbb{Z} or \Z.

The Set of Non-Zero Integers
$$\Z^*$$

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

Its LaTeX code 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.

Its LaTeX code is \mathbb{Z}'_m or \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 $$n$$.

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 $$\N^*_n$$.

Its LaTeX code is Z \left({n}\right).