0

Zero is the integer that represents the absence of quantity and serves as the additive identity in arithmetic. It is the origin on the number line, marking the point between positive and negative values, and it underpins place-value numeral systems, computation, and many mathematical concepts.

The word zero comes from the French zéero and Italian zero, ultimately deriving from Arabic sifr, meaning “empty,” and from Sanskrit śūnya, meaning “void.” The concept circulated in the West through translations of Arabic and Indian works in the Middle Ages. Early numeral systems used placeholders to indicate a lack of a digit in a given position, but treating zero as a number with defined rules took longer to develop, notably in Indian mathematics with Brahmagupta’s formal rules for zero and operations.

In representation, zero is the digit 0 in the decimal system and a binary digit in computing. In other cultures, symbols for zero vary, with words such as 零 (ling) in Chinese and ゼロ (zero) in Japanese. Zero enables a consistent place-value system and is essential for defining expansion, limits, and continuity in mathematics. It is the only integer that is neither positive nor negative and has no multiplicative inverse in standard arithmetic. It is the additive identity: adding zero to any number leaves that number unchanged.

Beyond pure math, zero has practical and scientific significance: absolute zero as a temperature reference, zero as a starting index in computer programming, and the empty set in set theory, whose cardinality is zero.