TeXipedia

Z

Represents the set of all integers (positive, negative, and zero) in mathematical notation.

Overview

Essential in number theory, abstract algebra, and general mathematics for denoting the fundamental integer number system.

  • Forms one of the basic number sets alongside natural numbers (N), real numbers (R), and complex numbers (C).
  • Crucial in ring theory, modular arithmetic, and discrete mathematics.
  • Commonly used when discussing divisibility, factors, and number-theoretic properties.
  • Appears frequently in computer science for describing integer data types and algorithmic constraints.

Examples

Denoting the set of all integers in a mathematical statement.

x∈Zx \in \Z 
x \in \Z

Specifying a range of integers in set-builder notation.

{n∈Z:−3≤n≤5}\{n \in \Z : -3 \leq n \leq 5\} 
\{n \in \Z : -3 \leq n \leq 5\}

Expressing a mapping between number sets in function notation.

f:Z→Z,f(x)=2x+1f: \Z \to \Z, \quad f(x) = 2x + 1 
f: \Z \to \Z, \quad f(x) = 2x + 1