The most common meaning of the term zero is the absence of any magnitude or quantity. For example, a person might say that he or she has zero children, meaning that he or she has no children. In this respect, zero is a number, like 2, +9, −45, or 0.392. It can be used in mathematical operations in nearly all of the same ways that nonzero numbers can be used. For example, 4 + 0 = 4 is a legitimate mathematical operation. One mathematical operation from which zero is omitted is division. One can divide 0 by any number (in which case the answer is always zero), but one cannot divide any number by zero. That is, the mathematical operation 4 ÷ 0 has no meaning.
Zeroes also have other functions. For example, a zero may indicate the beginning of some counting system. A temperature of zero degrees kelvin (0 K), for example, is the starting point for the absolute temperature scale.
Zero also is used as a placeholder in the Hindu-Arabic numeration system. The zero in the number 405 means that the number contains no tens. An expanded definition of the number is that 405 = 4 hundreds (4 × 100) plus 0 tens (0 × 10) plus 5 ones (5 × 1).
The history of the zero in numeration systems is a fascinating one. The symbol for zero (0) was not used by early Greek, Roman, Chinese, Egyptian, and other civilizations because they did not need it. In the Roman numeration system, for example, the number 405 is represented by CDIV.
The symbol for zero is believed to have first been used in the fourth century B.C. by an unknown Indian mathematician. When he wanted to record a more permanent answer on his beaded counting board, he used a simple dot. This dot was called a sunya and indicated columns in which there were no beads. While the sunya was not a true zero symbol, its use in place value notation was very important.
The actual 0 symbol for zero first appeared in about A.D. 800 when it was adopted as part of the Hindu-Arabic numeration system. The symbol was originally a dot, or sifr, as it was called in Arabic. Over time, the dot gradually evolved to a small circle and then to the familiar oval we recognize today.
The zero symbol reached Europe around the twelfth century. However, Europeans did not adopt the symbol eagerly. In fact, many were reluctant to abandon their familiar Roman numerals, and hostile battles took place between supporters of the two systems. Such battles sometimes took the form of bloody physical encounters. It was not until three centuries later, therefore, that the Hindu-Arabic numeration system—including the zero—was widely accepted and adopted throughout Europe.
[ See also Numeration systems ]