|Numbers first developed from the needs of counting, from the need to ensure that you were not being cheated in a deal, from the need to have some idea of the size of your possessions. Obviously, if you had none of something, there was no need to count it. Why would anyone list â€˜no elephantsâ€™ with the rest of their possessions? For this reason, there was no number representing none of something.
For counting alone, the lack of a representation for nothing is not important. However, for more complicated transactions, the concept becomes more vital. Even so, although there were words for none of something, the â€˜noneâ€™ did not reach the status of a number itself. In English, the answer to a question of number is still usually â€˜noneâ€™ rather than â€˜zeroâ€™.
Indian mathematicians were the first to recognize zero as a number. This recognition lay at the basis of their invention of the place notation for numbers (see number systems). Without zero, it is impossible to distinguish, for example, the numbers 2190 and 2019 using place notationâ€”this is probably the reason why no-one developed such systems earlier. The recognition of zero as a number in its own right lay at the basis of one of the most fundamental changes in the way that numbers are used, and, through the way that calculation was eased, paved the way for subsequent developments in mathematics.
Today, zero is often considered the most important number. It lies at the basis of the axiomatization of arithmetic by Peano; it is the number which is the most important in the integers looked at as a group or a ring, being the identity for addition (that is, you can add it to any number without changing the value of the number). SMcL