0 (number)

Zero is the integer representing no quantity and the additive identity: adding it to any integer leaves that integer unchanged.

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Natural number: A number used for counting or ordering; conventions differ on whether zero is included. Whether zero belongs to the natural numbers depends on the convention being used.
Additive identity: An element that leaves every element of a structure unchanged when added to it. Zero has this defining property for the integers.
Babylonian mathematics: The mathematical tradition of ancient Mesopotamia, known for its sexagesimal place-value system. Babylonian scribes used a placeholder mark in some positional numerals, not a fully developed zero number.
Place-value notation: A numeral system in which a digit’s value depends on its position. Zero holds empty positions, distinguishing numbers such as 205 from 25.
One: The integer immediately after zero and the multiplicative identity of the integers. One preserves values under multiplication, whereas zero preserves them under addition.
Integer: A whole number, its negative, or zero. Zero is one member of the integers, alongside positive and negative whole numbers.
Multiplicative zero: An element whose product with any element of a structure is zero. Zero absorbs every integer under multiplication.
Brahmagupta: An Indian mathematician who stated arithmetic rules for zero and negative numbers in the seventh century. His work gave zero explicit arithmetic treatment as a number.
Coordinate system: A method for assigning numerical positions to points using ordered values. Zero commonly marks the origin from which coordinates are measured.
Negative number: A real number less than zero. Negative integers lie on zero’s opposite side from positive integers.