mathbbN

The symbol mathbbN is commonly used in mathematics to denote the set of natural numbers. There is no universal agreement on whether the natural numbers include zero or start from one. In set theory and logic, it is customary to include zero, so mathbbN = {0, 1, 2, 3, ...}. In other branches of mathematics, such as number theory, it is more common to exclude zero, with mathbbN = {1, 2, 3, ...}. To avoid ambiguity, it is often specified whether zero is included or not. Some authors use mathbbN_0 or mathbbN union {0} to explicitly denote the set including zero, and mathbbN^* or mathbbN \ {0} to denote the set excluding zero. The set of natural numbers is fundamental in many areas of mathematics, including arithmetic, set theory, and computability theory. It is the smallest inductive set under the successor function. Operations such as addition and multiplication are defined on the natural numbers.