mathbbN0

mathbbN0, also written as N0 or N with a subscript 0, refers to the set of natural numbers including zero. It is a fundamental concept in mathematics, particularly in set theory and number theory. The set can be defined as:

mathbbN0 = {0, 1, 2, 3, ...}

This set is distinct from the set of natural numbers (mathbbN), which excludes zero. The inclusion of zero in emathbbN0 is significant in various mathematical contexts, such as in the definition of the factorial function, where 0! is defined as 1. It is also used in combinatorics, where emathbbN0 is often used to represent the number of ways to choose 0 elements from a set.

In some mathematical texts, emathbbN0 may be denoted as emathbbN* or emathbbN+ to emphasize the inclusion of zero. However, the notation emathbbN0 is more commonly used and is recognized as the standard notation for this set.