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zero

Zero is the integer, denoted 0, which, when used as a counting number, indicates that no objects are present. It is the only integer that is neither negative nor positive: it is smaller than any positive number but larger than any finite negative number. It obeys

x ± 0 = x
x × 0 = 0
0/x = 0
x0 = 1.

Division by zero is an undefined operation. Zero may be regarded as the identity element for addition in the field of real numbers.

Zero is both a number and a numeral. The number zero is the size of the empty set but it is not the empty set itself, nor is it the same thing as nothing. The numeral or digit zero is used in positional number systems, where the position of a digit signifies its value, with successive positions having higher values, and the digit zero is used to skip a position.

Zero in history

The earliest roots of the numeral zero stretch back 5,000 years to the Sumerians in Mesopotamia, who inserted a slanted double wedge between cuneiform characters for numbers, written positionally, to indicate a number's absence. The symbol changed over time as positional notation made its way to India, via the Greeks (in whose own culture zero made a late and only occasional appearance). Our word "zero" derives from the Hindi sunya for "void" or "emptiness," through the Arabic sifr, (which also gives us "cipher") and the Italian zevero. As a number in its own right, aside from it use as a position marker, zero took a much longer time to become established, and even now is not equal in status to other numbers: division by zero is not allowed.