This site is supported by donations to The OEIS Foundation.

One

From OeisWiki

(Redirected from 1)
Jump to: navigation, search

This article page is a stub, please help by expanding it.


The concept of one has many synonyms

  • Unity
  • Unique
  • Monad
  • ...

Contents

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

Properties of 1

The identity matrix

(...)

See also

External links

Personal tools