Natural numbers

The natural numbers are the set $\mathbb{N}=\{0,1,2,\dots\}$. (Some authors use $\{1,2,3,\dots\}$ instead; when needed, the chosen convention should be stated.)

Natural numbers are used to index a sequence and to formulate principles such as mathematical induction and the well-ordering principle . They embed naturally into the integers .

Examples:

• The numbers $0,1,2,3$ are elements of $\mathbb{N}$.
• The subset $\{n\in\mathbb{N} : n \text{ is even}\}$ is an infinite subset of $\mathbb{N}$.