1

1 (one, unit, unity) is a number a single unit of counting or measurement. It is generally used as a standard mathematical length, for example, the unit vector is a vector of length 1.

1 is the first nonzero natural number and the first and smallest positive integer. This fundamental property has led to its unique uses in other fields, ranging from science to sports. It commonly denotes the first, leading, or top thing in a group.

A fundamental mathematical property of 1 is to be a multiplicative identity, meaning that any number multiplied by 1 equals the same number. Most if not all properties of 1 can be deduced from this. In advanced mathematics, a multiplicative identity is often denoted 1, even if it is not a number.

1 is by convention not considered a prime number; this was not universally accepted until the mid-20th century. Additionally, 1 is the smallest possible difference between two distinct natural numbers.