2 (the number)
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. For integers written in a numeral system based on an even number, such as decimal and hexadecimal, divisibility by 2 is easily tested by merely looking at the one's place digit. If it's even, then the whole number is even.
Two is the smallest and the first prime number, and the only even one. The next prime is three. Despite being a prime, two is also a highly composite number, because it has more divisors than one. The next highly composite number is four.
Two 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
Powers of 2 are central to the concept of Mersenne primes.
Taking the square root of a number is such a common mathematical operation, that the spot on the root sign where the exponent would normally be written for cubic roots and other such roots, is left blank for square roots, as it is considered tacit.
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.
Two is a primorial, as well as its own factorial. Two often occurs in numerical sequences, such as the Fibonacci number sequence, but not quite as often as one does. Two is also a Motzkin number, and a Bell number.
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 Hegelian 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.
Other fields
Groups of two:
Two is:
See also: zero, one, two, three, four, integer, list of numbers.
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