TeXipedia

N

Represents the set of natural numbers (positive integers) in mathematical notation.

Overview

Essential in number theory, discrete mathematics, and general mathematical proofs where counting numbers are involved.

  • Commonly used in mathematical induction and sequence definitions
  • Appears frequently in computer science for algorithm analysis and loop indices
  • Often employed in combinatorics and set theory problems
  • Can be modified with subscripts or superscripts to denote specific subsets of natural numbers

Examples

Denoting the set of natural numbers in a mathematical statement.

x∈Nx \in \N 
x \in \N

Specifying the domain in a function definition.

f:N→N,f(n)=n2f: \N \to \N, \quad f(n) = n^2 
f: \N \to \N, \quad f(n) = n^2

Using natural numbers in a set-builder notation.

{n∈N:n is prime}\{n \in \N : n \text{ is prime}\} 
\{n \in \N : n \text{ is prime}\}