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2 (number)

From Academic Kids

(Redirected from Pair)
This article discusses the number two. For the year 2 AD, see 2.
II redirects here. II also stands for illegal immigrant.
<tr><td>Hebrew<td>ב (Bet)
Template:Numbers (digits)
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)

twi- (Old English)

Binary 10
Octal 2
Duodecimal 2
Hexadecimal 2

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

Contents

Evolution of the glyph

Image:Evolution2glyph.png

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, Missing image
TextFigs256.png
Image:TextFigs256.png

.

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, and the first Smarandache-Wellin prime. 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

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 Znm's problem start with 2.

In science

Two is:

In astronomy,

Messier object M2, a magnitude 6.5 globular cluster in the constellation Aquarius.
The New General Catalogue object (http://www.ngcic.org/) NGC 2, a magnitude 14.2 spiral galaxy in the constellation Pegasus
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/SEsaros/SEsaros1-175.html) of the solar eclipse series which began on -2861 May 4 and ended on -1563 June 21 . The duration of Saros series 2 was 1298.1 years, and it contained 73 solar eclipses.
The Saros number (http://sunearth.gsfc.nasa.gov/eclipse/LEsaros/LEsaros1-175.html) of the lunar eclipse series which began on -2541 February 21 and ended on -1225 April 22. The duration of Saros series 2 was 1316.2 years, and it contained 74 lunar eclipses.

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, r) 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.

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

In other fields

Groups of two:

Two is:

da:2 (tal) de:Zwei es:Dos eo:Du fr:2 (nombre) he:2 (מספר) ia:2 it:Due ja:2 ko:2 la:2 nah:Ome nl:Twee no:2 (tall) nn:Talet 2 pt:Dois simple:Two sl:2 (število) fi:2 (luku) sv:Tv th:2 (จำนวน) zh:2

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