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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 20

th 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 20

th century) now accepted by most mathematicians.

### Properties of 1

## The identity matrix

The

identity matrix is a

square matrix that has

1’s along the main diagonal and

0’s for all other entries. This matrix is often written simply as

, and is special in that it acts like

1 in

matrix multiplication.

Examples:

*I*1 = , *I*2 = , *I*3 = , *I*4 = 1 | | 0 | | 0 | | 0 |
0 | | 1 | | 0 | | 0 |
0 | | 0 | | 1 | | 0 |
0 | | 0 | | 0 | | 1 | |
, *I*5 = 1 | | 0 | | 0 | | 0 | | 0 |
0 | | 1 | | 0 | | 0 | | 0 |
0 | | 0 | | 1 | | 0 | | 0 |
0 | | 0 | | 0 | | 1 | | 0 |
0 | | 0 | | 0 | | 0 | | 1 | |
, ... |

## See also

## External links