2 (two) is a
number
A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can be represented in language with number words. More universally, individual numbers c ...
,
numeral and
digit. It is the
natural number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country").
Numbers used for counting are called ''cardinal ...
following
1 and preceding
3. It is the smallest and only even
prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
. Because it forms the basis of a
duality, it has
religious
Religion is usually defined as a social- cultural system of designated behaviors and practices, morals, beliefs, worldviews, texts, sanctified places, prophecies, ethics, or organizations, that generally relates humanity to supernatur ...
and
spiritual significance in many
cultures
Culture () is an umbrella term which encompasses the social behavior, institutions, and norms found in human societies, as well as the knowledge, beliefs, arts, laws, customs, capabilities, and habits of the individuals in these groups.Tylo ...
.
Evolution
Arabic digit
The digit used in the modern Western world to represent the number 2 traces its roots back to the Indic
Brahmic script
The Brahmic scripts, also known as Indic scripts, are a family of abugida writing systems. They are used throughout the Indian subcontinent, Southeast Asia and parts of East Asia. They are descended from the Brahmi script of ancient India ...
, where "2" was written as two horizontal lines. The modern
Chinese
Chinese can refer to:
* Something related to China
* Chinese people, people of Chinese nationality, citizenship, and/or ethnicity
**''Zhonghua minzu'', the supra-ethnic concept of the Chinese nation
** List of ethnic groups in China, people of ...
and
Japanese
Japanese may refer to:
* Something from or related to Japan, an island country in East Asia
* Japanese language, spoken mainly in Japan
* Japanese people, the ethnic group that identifies with Japan through ancestry or culture
** Japanese diaspor ...
languages (and Korean
Hanja
Hanja (Hangul: ; Hanja: , ), alternatively known as Hancha, are Chinese characters () used in the writing of Korean. Hanja was used as early as the Gojoseon period, the first ever Korean kingdom.
(, ) refers to Sino-Korean vocabulary, ...
) still use this method. The
Gupta script rotated the two lines 45 degrees, making them diagonal. The top line was sometimes also shortened and had its bottom end curve towards the center of the bottom line. In the
Nagari script, the top line was written more like a curve connecting to the bottom line. In the Arabic
Ghubar writing, the bottom line was completely vertical, and the digit 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 digit.
In fonts with
text figures
Text figures (also known as non-lining, lowercase, old style, ranging, hanging, medieval, billing, or antique figures or numerals) are numerals designed with varying heights in a fashion that resembles a typical line of running text, hence the ...
, digit 2 usually is of
x-height
upright 2.0, alt=A diagram showing the line terms used in typography
In typography, the x-height, or corpus size, is the distance between the baseline and the mean line of lowercase letters in a typeface. Typically, this is the height of the le ...
, for example, .
Etymology of ''two''
The word ''two'' is derived from the
Old English
Old English (, ), or Anglo-Saxon, is the earliest recorded form of the English language, spoken in England and southern and eastern Scotland in the early Middle Ages. It was brought to Great Britain by Anglo-Saxon settlers in the mid-5th c ...
words (
feminine), (neuter), and (masculine, which survives today in the form
twain
Twain may refer to:
People
* Mark Twain, pen name of American writer Samuel Langhorne Clemens (1835–1910)
* Norman Twain (1930–2016), American film producer
* Shania Twain (born 1965), Canadian singer-songwriter
Places
* Twain, California, a ...
).
The pronunciation , like that of ''who'' is due to the
labialization of the vowel by the ''w'' (combare from
womb
The uterus (from Latin ''uterus'', plural ''uteri'') or womb () is the organ in the reproductive system of most female mammals, including humans that accommodates the embryonic and fetal development of one or more embryos until birth. The ut ...
), which then disappeared before the related sound. The successive stages of pronunciation for the Old English would thus be , , , , and finally .
[
]
In mathematics
An integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...
is called ''even
Even may refer to:
General
* Even (given name), a Norwegian male personal name
* Even (surname)
* Even (people), an ethnic group from Siberia and Russian Far East
** Even language, a language spoken by the Evens
* Odd and Even, a solitaire game w ...
'' if it is divisible by 2. For integers written in a numeral system based on an even number, such as decimal, hexadecimal, or in any other base that is even, divisibility by 2 is easily tested by merely looking at the last digit. If it is even, then the whole number is even. In particular, when written in the decimal system, all multiples of 2 will end in 0, 2, 4, 6, or 8.
Two is the smallest prime number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways ...
, and the only even prime number, and for this reason it is sometimes called "the oddest prime". As the smallest prime number, it is also the smallest non-zero pronic number A pronic number is a number that is the product of two consecutive integers, that is, a number of the form n(n+1).. The study of these numbers dates back to Aristotle. They are also called oblong numbers, heteromecic numbers,. or rectangular number ...
, and the only pronic prime. The next prime is three
3 is a number, numeral, and glyph.
3, three, or III may also refer to:
* AD 3, the third year of the AD era
* 3 BC, the third year before the AD era
* March, the third month
Books
* '' Three of Them'' (Russian: ', literally, "three"), a 1901 ...
, which makes two and three the only two consecutive prime numbers. Two is the first prime number that does not have a proper twin prime
A twin prime is a prime number that is either 2 less or 2 more than another prime number—for example, either member of the twin prime pair (41, 43). In other words, a twin prime is a prime that has a prime gap of two. Sometimes the term ''twin p ...
with a difference two, while three is the first such prime number to have a twin prime. In consequence, the first pair of twin primes, three and five, encase four
4 (four) is a number, numeral and digit. It is the natural number following 3 and preceding 5. It is the smallest semiprime and composite number, and is considered unlucky in many East Asian cultures.
In mathematics
Four is the smallest c ...
in-between, which is the square
In Euclidean geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90- degree angles, π/2 radian angles, or right angles). It can also be defined as a rectangle with two equal-length a ...
of two, or .
Two is the first Sophie Germain prime
In number theory, a prime number ''p'' is a if 2''p'' + 1 is also prime. The number 2''p'' + 1 associated with a Sophie Germain prime is called a . For example, 11 is a Sophie Germain prime and 2 × 11 +  ...
, the first factorial prime
A factorial prime is a prime number that is one less or one more than a factorial (all factorials greater than 1 are even).
The first 10 factorial primes (for ''n'' = 1, 2, 3, 4, 6, 7, 11, 12, 14) are :
: 2 (0! +&n ...
, the first Lucas prime
The Lucas numbers or Lucas series are an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci numbers. Lucas numbers and Fibonacci nu ...
, and the first Ramanujan prime. Two is a Motzkin number
In mathematics, the th Motzkin number is the number of different ways of drawing non-intersecting chords between points on a circle (not necessarily touching every point by a chord). The Motzkin numbers are named after Theodore Motzkin and have d ...
, a Bell number
In combinatorial mathematics, the Bell numbers count the possible partitions of a set. These numbers have been studied by mathematicians since the 19th century, and their roots go back to medieval Japan. In an example of Stigler's law of eponymy ...
, an all-Harshad number, a meandric number, a semi-meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges.
Meander
Given a fixed oriented li ...
, and an open meandric number In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges.
Meander
Given a fixed oriented li ...
. It is also the third (or fourth) Fibonacci number
In mathematics, the Fibonacci numbers, commonly denoted , form a sequence, the Fibonacci sequence, in which each number is the sum of the two preceding ones. The sequence commonly starts from 0 and 1, although some authors start the sequence from ...
.
Two is the base of the binary system, the numeral system
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.
The same sequence of symbo ...
with the fewest tokens that allows denoting a natural number substantially more concisely (with tokens) than a direct representation by the corresponding count of a single token (with tokens). This binary number system is used extensively in computing
Computing is any goal-oriented activity requiring, benefiting from, or creating computing machinery. It includes the study and experimentation of algorithmic processes, and development of both hardware and software. Computing has scientific, ...
.
For any number ''x'':
:''x'' + ''x'' = 2 · ''x'' addition to multiplication
:''x'' · ''x'' = ''x''2 multiplication to exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to r ...
:''x''''x'' = ''x''↑↑2 exponentiation
Exponentiation is a mathematical operation, written as , involving two numbers, the '' base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". When is a positive integer, exponentiation corresponds to r ...
to tetration
In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though \uparrow \uparrow and the left-exponent ''xb'' are common.
Under the definition as rep ...
Extending this sequence of operations by introducing the notion of hyperoperation
In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called ''hyperoperations'' in this context) that starts with a unary operation (the successor function with ''n'' = 0). The sequence continues with ...
s, here denoted by "hyper(''a'',''b'',''c'')" with ''a'' and ''c'' being the first and second operand, and ''b'' being the ''level'' in the above sketched sequence of operations, the following holds in general:
:hyper(''x'',''n'',''x'') = hyper(''x'',(''n'' + 1),2).
Two has therefore the unique property that , disregarding the level of the hyperoperation, here denoted by Knuth's up-arrow notation
In mathematics, Knuth's up-arrow notation is a method of notation for very large integers, introduced by Donald Knuth in 1976.
In his 1947 paper, R. L. Goodstein introduced the specific sequence of operations that are now called ''hyperoperati ...
. The number of up-arrows refers to the level of the hyperoperation.
Two is the only number ''x'' such that the sum of the reciprocals of the natural powers of ''x'' equals itself. In symbols,
:
This comes from the fact that:
:
A Cantor space In mathematics, a Cantor space, named for Georg Cantor, is a topological abstraction of the classical Cantor set: a topological space is a Cantor space if it is homeomorphic to the Cantor set. In set theory, the topological space 2ω is called "the ...
is a topological space
In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance. More specifically, a topological space is a set whose elements are called po ...
homeomorphic to the Cantor set. The countably infinite
Infinite may refer to:
Mathematics
* Infinite set, a set that is not a finite set
*Infinity, an abstract concept describing something without any limit
Music
*Infinite (group), a South Korean boy band
*''Infinite'' (EP), debut EP of American m ...
product topology
In topology and related areas of mathematics, a product space is the Cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more natural-s ...
of the simplest discrete two-point space In topology
In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, wit ...
, , is the traditional elementary example.
The sum of the reciprocals of all non-zero triangular number
A triangular number or triangle number counts objects arranged in an equilateral triangle. Triangular numbers are a type of figurate number, other examples being square numbers and cube numbers. The th triangular number is the number of dots i ...
s converges to .
Powers of two
A power of two is a number of the form where is an integer, that is, the result of exponentiation with number two as the base and integer as the exponent.
In a context where only integers are considered, is restricted to non-negative ...
are central to the concept of Mersenne prime
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 17th ...
s, and important to computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...
. Two is the first Mersenne prime exponent.
Taking the square root
In mathematics, a square root of a number is a number such that ; in other words, a number whose ''square'' (the result of multiplying the number by itself, or ⋅ ) is . For example, 4 and −4 are square roots of 16, because .
...
of a number is such a common mathematical operation, that the spot on the root sign where the index would normally be written for cubic and other roots, may simply be left blank for square roots, as it is tacitly understood.
The square root of 2 was the first known irrational number
In mathematics, the irrational numbers (from in- prefix assimilated to ir- (negative prefix, privative) + rational) are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two inte ...
.
The smallest field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
has two elements.
In a set-theoretical construction of the natural numbers, 2 is identified with the set . This latter set is important in category theory: it is a subobject classifier In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object ''X'' in the category correspond to the morphisms from ''X'' to Ω. In typical examples, that morphism assigns "true ...
in the category of sets.
Two consecutive twos (as in "22" for "two twos"), or equivalently "2-2", is the only fixed point of John Conway's look-and-say function. This in contrast, for example, with "1211", which would read as "one 1, one 2, and two 1s" or "111221".
There are no 2 x 2 magic squares; they also can be defined as the only null
Null may refer to:
Science, technology, and mathematics Computing
* Null (SQL) (or NULL), a special marker and keyword in SQL indicating that something has no value
* Null character, the zero-valued ASCII character, also designated by , often use ...
by magic square set.
Two also has the unique property such that,
:
and also, with ''a'' not equal to zero,
:.
In any ''n''-dimensional, euclidean space two distinct points determine a line.
In two dimensions, a digon
In geometry, a digon is a polygon with two sides (edges) and two vertices. Its construction is degenerate in a Euclidean plane because either the two sides would coincide or one or both would have to be curved; however, it can be easily visu ...
is a polygon with two sides (or edges) and two vertices. On a circle, it is a tessellation
A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to higher dimensions and a variety o ...
with two antipodal points and 180° arc edges.
The simplest tessellation in two-dimensional space
In mathematics, a plane is a Euclidean ( flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as ...
, though an improper tessellation, is that of two -sided apeirogon
In geometry, an apeirogon () or infinite polygon is a generalized polygon with a countably infinite number of sides. Apeirogons are the two-dimensional case of infinite polytopes.
In some literature, the term "apeirogon" may refer only to th ...
s joined along all their edges, coincident about a line that divides the plane
Plane(s) most often refers to:
* Aero- or airplane, a powered, fixed-wing aircraft
* Plane (geometry), a flat, 2-dimensional surface
Plane or planes may also refer to:
Biology
* Plane (tree) or ''Platanus'', wetland native plant
* ''Planes' ...
in two. This order-2 apeirogonal tiling
In geometry, an order-2 apeirogonal tiling, apeirogonal dihedron, or infinite dihedronConway (2008), p. 263 is a tiling of the plane consisting of two apeirogons. It may be considered an improper regular tiling of the Euclidean plane, with Sch ...
is the arithmetic limit of the family of dihedra
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of ''n'' edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat ...
.
For any polyhedron homeomorphic to a sphere, the Euler characteristic is , where ''V'' is the number of vertices, ''E'' is the number of edge
Edge or EDGE may refer to:
Technology Computing
* Edge computing, a network load-balancing system
* Edge device, an entry point to a computer network
* Adobe Edge, a graphical development application
* Microsoft Edge, a web browser developed ...
s, and ''F'' is the number of face
The face is the front of an animal's head that features the eyes, nose and mouth, and through which animals express many of their emotions. The face is crucial for human identity, and damage such as scarring or developmental deformities may aff ...
s.
The long diagonal of a regular hexagon
In geometry, a hexagon (from Greek , , meaning "six", and , , meaning "corner, angle") is a six-sided polygon. The total of the internal angles of any simple (non-self-intersecting) hexagon is 720°.
Regular hexagon
A '' regular hexagon'' has ...
is of length two when its sides are of unit length. Whereas a square of unit side length has a diagonal equal to the square root of two
The square root of 2 (approximately 1.4142) is a positive real number that, when multiplied by itself, equals the number 2. It may be written in mathematics as \sqrt or 2^, and is an algebraic number. Technically, it should be called the princi ...
, and a cube of unit side length has a space diagonal
In geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with '' face diagonals'', which connect vertices on the same face (bu ...
equal to the square root of three, a space diagonal inside a tesseract
In geometry, a tesseract is the four-dimensional analogue of the cube; the tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of six square faces, the hypersurface of the tesseract consists of e ...
measures two when its side lengths are of length one.
There are two known sublime numbers, which are numbers with a perfect number of factors, whose sum itself yields a perfect number
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number.
...
. 12 is one of the two sublime numbers, with the other being 76 digits long.
In science
*The number of polynucleotide
A polynucleotide molecule is a biopolymer composed of 13 or more nucleotide monomers covalently bonded in a chain. DNA (deoxyribonucleic acid) and RNA (ribonucleic acid) are examples of polynucleotides with distinct biological function. The pre ...
strands in a DNA double helix
A double is a look-alike or doppelgänger; one person or being that resembles another.
Double, The Double or Dubble may also refer to:
Film and television
* Double (filmmaking), someone who substitutes for the credited actor of a character
* ...
.
*The first magic number.
*The atomic number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every ...
of helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
.
*The ASCII
ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because ...
code of "Start of Text
The C0 and C1 control code or control character sets define control codes for use in text by computer systems that use ASCII and derivatives of ASCII. The codes represent additional information about the text, such as the position of a cursor, ...
".
*2 Pallas
Pallas ( minor-planet designation: 2 Pallas) is the second asteroid to have been discovered, after Ceres. It is believed to have a mineral composition similar to carbonaceous chondrite meteorites, like Ceres, though significantly less hy ...
, a large asteroid in the main belt and the second asteroid ever to be discovered.
*The Roman numeral II (usually) stands for the second-discovered satellite of a planet or minor planet (e.g. Pluto II
Nix is a natural satellite of Pluto, with a diameter of across its longest dimension. It was discovered along with Pluto's outermost moon Hydra on 15 May 2005 by astronomers using the Hubble Space Telescope, and was named after Nyx, the Gr ...
or (87) Sylvia II Remus).
*A binary star is a stellar system
A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a ''star cluster'' or ''galaxy'', although, broadly speaking, ...
consisting of two stars orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
ing around their center of mass.
*The number of brain
A brain is an organ that serves as the center of the nervous system in all vertebrate and most invertebrate animals. It is located in the head, usually close to the sensory organs for senses such as vision. It is the most complex organ in a ve ...
and cerebellar
The cerebellum (Latin for "little brain") is a major feature of the hindbrain of all vertebrates. Although usually smaller than the cerebrum, in some animals such as the mormyrid fishes it may be as large as or even larger. In humans, the cereb ...
hemispheres.
In sports
*The number of points scored on a safety
Safety is the state of being "safe", the condition of being protected from harm or other danger. Safety can also refer to the control of recognized hazards in order to achieve an acceptable level of risk.
Meanings
There are two slightly dif ...
in American football
American football (referred to simply as football in the United States and Canada), also known as gridiron, is a team sport played by two teams of eleven players on a rectangular field with goalposts at each end. The offense, the team wi ...
*A field goal inside the three-point line is worth two points in basketball
Basketball is a team sport in which two teams, most commonly of five players each, opposing one another on a rectangular court, compete with the primary objective of shooting a basketball (approximately in diameter) through the defender's h ...
.
*The two in basketball is called the Shooting Guard
*2 represents the catcher
Catcher is a position in baseball and softball. When a batter takes their turn to hit, the catcher crouches behind home plate, in front of the ( home) umpire, and receives the ball from the pitcher. In addition to this primary duty, the ca ...
position in baseball
Baseball is a bat-and-ball sport played between two teams of nine players each, taking turns batting and fielding. The game occurs over the course of several plays, with each play generally beginning when a player on the fielding t ...
.
Other
In pre-1972 Indonesian and Malay orthography, ''2'' was shorthand for the reduplication that forms plurals: ''orang'' (person), ''orang-orang'' or ''orang2'' (people). In Astrology
Astrology is a range of divinatory practices, recognized as pseudoscientific since the 18th century, that claim to discern information about human affairs and terrestrial events by studying the apparent positions of celestial objects. Di ...
, Taurus
Taurus is Latin for 'bull' and may refer to:
* Taurus (astrology), the astrological sign
* Taurus (constellation), one of the constellations of the zodiac
* Taurus (mythology), one of two Greek mythological characters named Taurus
* '' Bos tauru ...
is the second sign of the Zodiac
The zodiac is a belt-shaped region of the sky that extends approximately 8° north or south (as measured in celestial latitude) of the ecliptic, the apparent path of the Sun across the celestial sphere over the course of the year. The pat ...
. For Pythagorean numerology (a pseudoscience
Pseudoscience consists of statements, beliefs, or practices that claim to be both scientific and factual but are incompatible with the scientific method. Pseudoscience is often characterized by contradictory, exaggerated or unfalsifiable clai ...
) the number 2 represents duality, the positive and negative poles that come into balance and seek harmony.
See also
*List of highways numbered 2
The following highways are numbered 2. For roads numbered A2, see list of A2 roads. For roads numbered B2, see list of B2 roads. For roads numbered M2, see list of M2 roads. For roads numbered N2, see list of N2 roads.
International
* AH2, As ...
* Binary number
References
External links
Prime curiosities: 2
{{DEFAULTSORT:2 (Number)
2 (number)
Integers