Definition · applies to numbers · also called positive integers, counting numbers, $\mathbb{N}$, $\mathbb{N}_+$, $\mathbb{Z}_{> 0}$

Elementary

The natural numbers are the counting numbers $1, 2, 3, 4, \dots$

Undergraduate

The natural numbers are the set $\lbrace 1, 2, 3, \dots \rbrace$ of positive integers, often written $\mathbb{N}$, \(\mathbb{Z}_{> 0}\), or \(\mathbb{N}_{+}\).

Notes

This convention is common in number theory and analysis. Compare natural numbers starting at 0.

Distinctions involving this term

  • Whole numbers vs. natural numbers: “Whole numbers” and “natural numbers” are used synonymously by some others to indicate all nonnegative integers, $0, 1, 2, 3, \dots$. “Whole numbers” is the usual name in primary schools, and “natural numbers” (or “nonnegative integers”) is the usual name in mathematics. “Natural numbers” is, however, used by some authors to indicate the non-negative integers, $1, 2, 3, \dots$ and “whole numbers” is used to indicate all integers, “$\dots, -2, -1, 0, 1, 2, \dots$.

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