two

Two is the natural number following one and preceding three; as an ordinal, it is the second. In numerals it is written as 2, in Roman numerals as II, and in words as “two.” The word derives from Old English twa, related to Proto-Germanic twa- and ultimately from the Proto-Indo-European root *duo- meaning “two.”

In mathematics, two is the smallest and the only even prime number, making it fundamental to the structure of the integers. All even numbers are multiples of two. The number two is the base of the binary numeral system, in which data are represented with two symbols: 0 and 1. It also indexes dimensions, notably two-dimensional space, and frequently conveys duality, pairing, or a couple, as in two items. The factorial of two is two (2!), and basic identities such as 2 × 2 = 4 and 1 + 1 = 2 reflect its role in arithmetic.

In science, diatomic molecules, such as O2 and N2, consist of two atoms. In logic and computer science, truth values are often represented as two states: true and false (binary logic).

In language and culture, the notion of two as a pair appears across traditions, often associated with balance, polarity, and complementarity. The prefixes duo- and dy- derive from the same Indo-European root and appear in numerous terms, reflecting the enduring association of two with pairing and cooperation.