0 (number)

Zero is a numeral representing the absence of quantity, that is, the count when nothing is being counted. It also functions as a placeholder in positional numeral systems, such as the decimal system, which distinguish the values of different digit positions; for example, 105 and 15 differ because of the zero present.

In mathematics, zero is a real number with no sign (it is neither positive nor negative). It is the identity element for addition: any number added to zero remains that number. In multiplication, any number multiplied by zero yields zero. Division by zero is undefined.

Mathematical properties

Zero is a member of the natural numbers according to modern mathematical convention, although some mathematical traditions begin counting from one. Zero is an even number. It marks the boundary between positive and negative numbers on the number line. As an exponent: any nonzero number raised to the power zero equals one.

History and development

Earlier systems, such as the Babylonian, used a placeholder symbol to distinguish digit positions, but it was not always an independent number. Indian mathematicians developed zero as a number with clear operational properties, and the system subsequently spread through Islamic scholarship and into Europe via translated mathematical texts. The Hindu-Arabic numeral system used worldwide today depends on the existence of zero.

Modern usage

In computing and electronics, zero and one are the two symbols of the binary system, which forms the foundation of data storage and processing. In science and engineering, zero commonly denotes an arbitrary starting point for measurement, such as zero degrees Celsius or the origin of a graph; at that reference point, zero is a chosen marker and does not represent true absence.