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One : Unique

One (1) is the natural number following zero and preceding two. 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).

1+1 can have over 10 different results: 0, 1, 2, 10, 110, 11, 10.01, 3, 1100 or "11".

One cannot be used as the base of a 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 the usual 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).

One isn't 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.

In the Von Neumann representation[?] of natural numbers, 1 is the set {0}. This set has cardinality 1 and hereditary rank[?] 1.

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.

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.

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)

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.

Quotes

There is a song lyric which goes: "One is the loneliest number..." [1] (http://www.ugcs.caltech.edu/~harel/cgi/page/htmlit?Aime_One.html&printer)

For the year AD 1, see 1
For the order of magnitude, see 1 E0[?]

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