Two

simple:Two

Two (2) is the natural number following one and preceding three.

Two has many properties in mathematics:

• An integer is called even if it is divisible by 2.
• Two is the smallest and the first prime number, and the only even one. The next prime is three.
• Two is also a highly composite number, even though it is prime rather than composite. The next highly composite number is four.
• 2 is a factor of 10, so fractions with 2 in the denominator do not yield infinite decimal expansions, as is the case with most primes.
• Two is the base of the simplest numeral system in which natural numbers can be written concisely, the binary system widely used in computers.
• For any number x:

x+x = 2·x

x·x = x²

• The smallest field has two elements.
• In the set-theoretical construction of the natural numbers, 2 is identified with the set {0,1}. This latter set is important in category theory: it is a subobject classifier in the category of sets.

In names of translation software, infix 2 often represents the word "to" with the connotation "translate to", as in dvi2ps (DVI to PostScript), int2string (integer to string) and texi2roff (Texinfo to troff).

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

• Two candles are lit on Finnish Independence Day. Putting them on the windowsill invokes the symbolical meaning of division, and thus independence.
• The yin-yang symbol in Chinese culture
• Two, or deuce, is the lowest number in a deck of cards (if you are playing with the ace high).
• The process of antithesis in Hegelian dialectic creates two-ness from one-ness
• In the philosophy of Pythagoras, the dyad is the second thing created (see the article monad for more on this)
• See dualism for a discussion of several other kinds of two-ness

Two is a good number in Chinese culture. There is a Chinese saying "good things come in pairs". It is common to use double symbols in product brandnames, e.g. double happiness, double coin, double elephants etc. Cantonese people like the number two because it sounds the same as the word "easy" (易) in Cantonese.

Two is also:

• the number of musicians in a duet.

Other usages include:

• Letter of the two sorries
• One country, two systems

The section about '2' in the meaning of 'to' contains material from FOLDOC's article on Two, used with permission.

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

This article is about the number. For the year, see 2. For some fictional characters, see Number Two.