# Zero

Zero (written 0) is the additive identity of the real numbers. One is the successor of zero. It is believed that Indians invented the numerical concept of zero for their trades to the west.

0 is the smallest number in the set of non-negative integers $\mathbb{N}_0 = \{0, 1, 2, 3, \ldots\}$.

Developed by Arab mathematicians, the concept of zero was an important development in mathematics as it provided an easy method to increase magnitude in a simple and consistent manner, a significant advance in the practice of arithmetic and a step towards more sophisticated mathematics.

In the BC/AD timeline of the Gregorian calendar, the year zero is omitted. History proceeds from December 31, 1 BC to January 1, AD 1. This can lead to counting errors when summing up spans of time that cross the transition point, because people often assume the timeline is constructed like the set of integers.