# 2 number

 0 10 20 30 40 50 60 70 80 90 >> Cardinal 2 two Ordinal 2nd second Numeral system binary Factorization prime Divisors 1, 2 Roman numeral II Unicode representation of Roman numeral Ⅱ, ⅱ prefixes di- (from Greek) duo- bi- (from Latin) Binary 10 Octal 2 Duodecimal 2 Hexadecimal 2 Hebrew ב (Bet)

2 (two) is a number, numeral, and glyph. It is the natural number following 1 and preceding 3.

## In mathematics

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. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, and the first Smarandache-Wellin prime. It is an Eisenstein prime with no imaginary part and real part of the form $\displaystyle 3n - 1$ . It is also a Stern prime, a Pell number, and a Markov number, appearing in infinitely many solutions to the Markov Diophantine equation involving odd-indexed Pell numbers.

Two is the third Fibonacci number, being the sum of the first two, 1 and 1.

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 vulgar 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
xx = x↑↑2 exponentiation to tetration

Two also has the unique property that 2+2 = 2·2 = 22.

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. With one exception, all known solutions to Znám's problem start with 2.

## The Arabic glyph

The glyph we use today in the Western world to represent the number 2 traces its roots back to the Brahmin Indians, who wrote 2 as two horizontal lines (it is still written that way in modern Chinese, and is analogous to the Roman numeral II). The Gupta rotated the two lines 45 degrees, making them diagonal, and sometimes also made the top line shorter and made its bottom end curve towards the center of the bottom line. Apparently for speed, the Nagari started making the top line more like a curve and connecting to the bottom line. The Ghubar Arabs made the bottom line completely vertical, and now the glyph looked like a dotless closing question mark. Restoring the bottom line to its original horizontal position, but keeping the top line as a curve that connects to the bottom line leads to our modern glyph.

In fonts with text figures, 2 usually has the same height as a lowercase X, for example, File:TextFigs256.png.

Two is:

In astronomy

## 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 numeral 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.

In rhetorics, hendiadys is a figure of speech where two words with similar or identical meanings are used where one would be sufficient.

Among children, or when otherwise calling for subtlety, the phrase "number 2" can refer to the act of defecating (with urination being "number 1").

## In sports

In rugby union, 2 is the number of the hooker. In baseball, two represents the catcher's position.

## In technology

Two is the DVD region in Europe, South Africa, the Middle East and Japan.

Two is the first digit of international telephone dialing codes primarily for countries in Africa. On most phones, the 2 key is associated with the letters A, B, and C, but on the BlackBerry it is the key for T and Y.

Groups of two:

Two is: