2 In mathematics

Two has many properties in mathematicsMathematics is commonly defined as the study of patterns of structure, change, and space; more informally, one might say it is the study of "figures and numbers". In the formalist view, it is the investigation of axiomatically defined abstract structures. An integerThe integers consist of the positive natural numbers (1, 2, 3, …) the negative natural numbers (−1, −2, −3,. and the number zero. The set of all integers is usually denoted in mathematics by Z (or Z in blackboard bold, ), which st 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 ten, 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 Addition to Multiplication

x·x = x² Multiplication to Exponentiation

x^x = x↑↑2 Exponentiation to Tetration

Powers of 2 are central to the concept of Mersenne primes, and important to computer science. 2 is the first Mersenne prime exponent.

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 square root of 2 was the first known irrational number.

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, a Bell number, an all-Harshad number, a meandric number, a semi-meandric number, and an open meandric number.

Two is the number of n-Queens Problem solutions for n = 4.

3 In human culture

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 (二, èr) 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 .

Words that can be used as synonyms for two include brace, couple, deuce, duet, pair, twain, and twins.

4 In science

Two is:

• The number of polynucleotide strands in a DNA double helix.
• The first Magic number (physics).
• The atomic number of helium.

5 In other fields

Groups of two:

• Lists of pairs
  • list of famous pairs
  • list of twins

Two is:

• The denomination of U.S. paper currency with Thomas Jefferson's portrait on it; (last issued 1996; as of 2004 rarely seen in general circulation).
• The denomination of the Canadian monetary coin featuring a polar bear.
• The demonination of the $2 New Zealand coin, featuring the white heron.
• The name of several fictional characters: Number Two.
• In the phrase "Number two", a euphemism for defecation.
• The designation of the Trans-Canada Highway in most of the province of New Brunswick.
• One of the radio callsign prefixes allocated to the United Kingdom.
• The DVD region in Europe, South Africa, the Middle East and Japan.
• In rugby union, the number of the hooker.
• In baseball, two represents the catcher's position.
• The years: A.D. 2, 2 B.C., 1902 or 2002. (The latter pair are more likely to be referred to as "oh-two".)
• The first digit of international telephone dialing codes primarily for countries in Africa.
• In music, the roman numeral ii is the supertonic scale degree, chord, or diatonic function, when distinguished II = major and ii = minor.

5.1 See also

Digit-letter combinations starting with 2:

• 2a 2b 2c 2d 2e 2f 2g 2h 2i 2j 2k 2l 2m 2n 2o 2p 2q 2r 2s 2t 2u 2v 2w 2x 2y 2z
• 2A 2B 2C 2D 2E 2F 2G 2H 2I 2J 2K 2L 2M 2N 2O 2P 2Q 2R 2S 2T 2U 2V 2W 2X 2Y 2Z

02 02 02 Ternary digits 02 02 02 02 02 02 02 02 02 Catalan_numbers Powers of 2 Hexadecimal digit

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