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# One

(Redirected from 1)

The concept of one has many synonyms

• Unity
• Unique
• ...

## 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 ${\displaystyle \scriptstyle n\,}$ is now considered prime if and only if it has exactly two divisors, a unit and a nonunit, where associates of ${\displaystyle \scriptstyle k\,}$ (i.e. product of some unit ${\displaystyle \scriptstyle u\,}$ with ${\displaystyle \scriptstyle k\,}$) 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.

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