One

simple:One

One (1) is the natural number following zero and preceding two. It represents a single entity. One is sometimes referred to as unity. The Roman numeral for one is I.

For any number x:

x·1 = 1·x = x (see Multiplication);
x/1 = x (see Division);
x¹ = x and 1^x = 1 (see Exponentiation).

Using ordinary addition, we have 1+1=2; depending on the interpretation of the symbol "+" and the numeral system used, the expression can have many different values, listed at One_plus_one.

One cannot be used as the base of a positional numeral system in the ordinary way. Sometimes tallying is referred to as "base 1", since only one mark (the tally) is needed, but this doesn't work in the same way as other positional numeral systems. Related to this, one cannot take logarithms with base 1 (same as one cannot divide by zero, since log_n x is log_e x / log_e n, and log 1 = 0).

In the Von Neumann representation of natural numbers, 1 is defined as the set {0}. This set has cardinality 1 and hereditary rank 1. Sets like this with a single element are called singletonss.

In a multiplicative group or monoid, the identity element is sometimes called 1, but e is more traditional. However, 1 is especially common for the multiplicative identity of a ring.

One is not always thought of as a number, although (unlike zero) it has been accepted as such since antiquity. Reflecting this, many languages retain a distinction between singular and plural forms of a noun, the former reserved for the case when only one object is being referred to.

Many human cultures have given the concept of one-ness symbolic meanings:

Many religions consider God to be a perfect example of one-ness
In playing cards, the one is the ace, which in many games is considered the highest card in the suit, rather than the lowest as one would normally expect.
See monad for a discussion of several other types of one-ness.

Something is unique if it is the only one of its kind. More loosely and exaggeratingly (especially in advertising) the term is used for something very special.

One is also:

The number of musicians in a solo.
The number of actors in a monologue or soliloquy.
The number of known Universes.
The number most often used for representing 'true' as a Boolean datatype in computer science (though any other number than zero would also represent true)
a song by U2
An (archaic) expression of the first person singular: "one is not amused".
An (archaic) expression of the second person singular: "does one take sugar?".
An enneagram personality type.

Quotes

There is a song lyric which goes: "One is the loneliest number..." [1]

See also: zero, one, two, integer, list of numbers, unity.

For the year AD 1, see 1
For the order of magnitude, see 1 E0