Two
- For the year 2, see 2. For some fictional characters, see Number Two.
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:
- 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.
Cultural meaning
The duality of all things is an important notion in most cultures and religions. The most common philosophical dichotomy is perhaps the one of good and evil, but there are many others. See dualism for an overview. In Hegelianian dialectic, the process of antithesis creates two perspectives from one.
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.
In Finland, two candles are lit on Independence Day. Putting them on the windowsill invokes the symbolical meaning of division, and thus independence.
In the philosophy of Pythagoras, the dyad is the second thing created (see the article monad for details).
The number 2 is sometimes used as a shorthand for "to". One common example is computer software which translates data from one format into another, such as dvi2ps and texi2roff.
See also: list of famous pairs, list of twins, zero, one, two, three, four, integer, list of numbers.
