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# Two

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

Two is the smallest and the first prime number, and the only even one, the next is three.

An integer is called even if it is divisible by 2, ie. $x\equiv 0 \mod 2$ if x is even.

Two is also a highly composite number. 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.

For any number x:

x+x = 2·x
x·x = x2

The smallest field has two elements.

Two is the base of the simplest numeral system in which natural numbers can be written concisely, the binary system widely used in computers.

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 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.

The section about '2' in the meaning of 'to' contains material from FOLDOC's article on Two (http://foldoc.doc.ic.ac.uk/foldoc/foldoc.cgi?2), used with permission.