The concept of one has many synonyms
The number one
One has sometimes not been considered a number in some cultures in the past (because it does not involve plurality.) The number one is represented by the numeral 1. 1 is the first positive integer and the first positive odd number.
Although 1 has been considered prime until the beginning of the 20th century (former definition: no divisors apart from 1 and itself, itself not necessarily distinct from 1) the unit (i.e. multiplicatively invertible element) 1 is now widely known as the empty product (defined as the multiplicative identity, i.e. 1) of primes, where an integer is now considered prime if and only if it has exactly two divisors, a unit and a nonunit, where associates of (i.e. product of some unit with ) are not considered distinct divisors. This is the definition (resulting from the development of abstract algebra at the turn of the 20th century) now accepted by most mathematicians.
Properties of 1
- Multiplicative identity (the empty product is defined as the multiplicative identity.)
- Unit (has a multiplicative inverse) in any number set.
- (the empty product, defined as the multiplicative identity.)
The identity matrix