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For other uses of "2", see 2 (disambiguation). 2 and two may mean 2 (number, a number numeral and glyph 2, the year 2 AD 2 BC, the year 2 BC
"II" redirects here. For other uses, see II (disambiguation).
2

0 1 2 3 4 5 6 7 8 9 →

0 10 20 30 40 50 60 70 80 90 →
Cardinal 2
two
Ordinal number 2nd
second
Numeral system binary
Factorization prime
Gaussian integer factorization (1 + i)(1 − i)
Divisors 1, 2
Greek numeral β'
Roman numeral II
Roman numeral (Unicode) Ⅱ, ⅱ
Arabic ٢
Ge'ez ፪
Bengali ২
Chinese numeral 二，貳
Devanāgarī २
Hebrew ב (Bet)
Khmer ២
Korean 이
Thai ๒
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. Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity ---- In mathematics Three is the first odd Prime number, and the second smallest prime In mathematics Four is the smallest Composite number, its proper Divisors being and. This article discusses the number five. For the year 5 AD see 5. In mathematics Six is the second smallest Composite number, its proper Divisors being 1, 2 and 3. In mathematics Seven is the fourth Prime number. It is not only a Mersenne prime (since 23 &minus 1 = 7 but also a In mathematics 8 is a Composite number, its Proper divisors being 1, 2, and 4. In mathematics Nine is a Composite number, its proper Divisors being 1 and 3. This is a list of articles about Numbers ( not about Numerals. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French "Twenty" redirects here For the village in England, see Twenty Lincolnshire. 30 ( thirty) is the Natural number following 29 and preceding 31. 40 ( forty) is the Natural number following 39 and preceding 41. This article discusses the number fifty. For the year 50 CE see 50. 60 ( sixty) is the Natural number following 59 and preceding 61. 70 ( seventy) is the Natural number following 69 and preceding 71. 80 ( eighty) is the Natural number following 79 and preceding 81. 90 ( ninety) is the Natural number preceded by 89 and followed by 91. This article describes cardinal numbers in mathematics For cardinals in linguistics see Names of numbers in English. In linguistics ordinal numbers are the words representing the rank of a number with respect to some order in particular order or position (i A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. In Mathematics, factorization ( also factorisation in British English) or factoring is the decomposition of an object (for In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 A Gaussian integer is a Complex number whose real and imaginary part are both Integers The Gaussian integers with ordinary addition and multiplication of complex In Mathematics, a divisor of an Integer n, also called a factor of n, is an integer which evenly divides n without ʹ the numeral sign redirects here For the accent ´ see Acute accent. Roman numerals are a Numeral system originating in ancient Rome, adapted from Etruscan numerals. Arabic (ar الْعَرَبيّة (informally ar عَرَبيْ) in terms of the number of speakers is the largest living member of the Semitic language Ge'ez (gez ግዕዝ) also called Ethiopic, is an Abugida script that was originally developed to write Ge'ez, a Semitic language Chinese numerals are characters for writing Numbers in Chinese. Khmer numerals are the numerals used in the Khmer language of Cambodia. The Korean language has two regularly used sets of numerals a Sino-Korean system and a native Korean system Thai numerals (เลขไทย are a set of numerals traditionally used in Thailand, although the Arabic numerals are more common Numerical prefixes are usually derived from the words for numbers in various languages most commonly Greek and Latin, although this is not always the case Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. The octal Numeral system, or oct for short is the base -8 number system and uses the digits 0 to 7 The duodecimal system (also known as base -12 or dozenal) is a Numeral system using twelve as its base. In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a A number is an Abstract object, tokens of which are Symbols used in Counting and measuring. A glyph is an element of writing Two or more glyphs representing the same symbol whether interchangeable or context-dependent are called Allographs the abstract unit they It is the natural number following 1 and preceding 3. In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an Mathematics For any number x: x ·1 = 1· x = x (1 is the multiplicative identity ---- In mathematics Three is the first odd Prime number, and the second smallest prime

Contents

In mathematics

Two has many properties in mathematics. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and [1] An integer is called even if it is divisible by 2. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French 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. The decimal ( base ten or occasionally denary) Numeral system has ten as its base. In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a 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 and the first prime number, and the only even one (for this reason it is sometimes humorously called "the oddest prime"). In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 The next prime is three. ---- In mathematics Three is the first odd Prime number, and the second smallest prime Two and three are the only two consecutive prime numbers. 2 is the first Sophie Germain prime, the first factorial prime, the first Lucas prime, and the first Smarandache-Wellin prime. In Number theory, a Prime number p is a Sophie Germain prime if 2 p  + 1 is also prime A factorial prime is a Prime number that is one less or one more than a Factorial (all factorials above 1 are even The Lucas numbers are an Integer sequence named after the mathematician François Édouard Anatole Lucas (1842&ndash1891 who studied both that sequence and the In Mathematics, a Smarandache-Wellin number is an Integer that in a given base is the Concatenation of the first n Prime numbers written It is an Eisenstein prime with no imaginary part and real part of the form 3n − 1. In Mathematics, an Eisenstein prime is an Eisenstein integer z = a + b\\omega\qquad(\omega = e^{2\pi i/3} that is irreducible 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. A Stern prime, named for Moritz Abraham Stern, is a Prime number that is not the sum of a smaller prime and twice the square of a nonzero Integer In Mathematics, the Pell numbers and companion Pell numbers (Pell-Lucas numbers are both sequences of Integers that have been known since ancient A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation

It is the third Fibonacci number, and the third and fifth Perrin numbers. In Mathematics, the Fibonacci numbers are a Sequence of numbers named after Leonardo of Pisa, known as Fibonacci In Mathematics, the Perrin numbers are defined by the Recurrence relation P (0 = 3 P (1 = 0 P (2 = 2

Despite being a prime, two is also a highly composite number, because it has more divisors than the number one. A highly composite number ( HCN) is a positive Integer with more Divisors than any smaller positive integer The next highly composite number is four. In mathematics Four is the smallest Composite number, its proper Divisors being and.

Vulgar fractions with 2 or 5 in the denominator do not yield infinite decimal expansions, as is the case with most primes, because 2 and 5 are factors of ten, the decimal base. In Mathematics, a fraction (from the Latin fractus, broken is a concept of a proportional relation between an object part and the object This article gives a mathematical definition For a more accessible article see Decimal. In Mathematics, a divisor of an Integer n, also called a factor of n, is an integer which evenly divides n without

Two is the base of the simplest numeral system in which natural numbers can be written concisely, being the length of the number a logarithm of the value of the number (whereas in base 1 the length of the number is the value of the number itself); the binary system is used in computers. In mathematical numeral systems, the base or radix is usually the number of unique digits, including zero that a positional Numeral A numeral system (or system of numeration) is a Mathematical notation for representing numbers of a given set by symbols in a consistent manner A computer is a Machine that manipulates data according to a list of instructions.

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=2↑↑2=2↑↑↑2, and so on, no matter how high the operation is. Addition is the mathematical process of putting things together In Mathematics, tetration (also known as hyper -4

Two is the only number x such that the sum of the reciprocals of the powers of x equals itself. In symbols: \sum_{k=0}^{\infin}\frac {1}{2^k}=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\cdots=2.

This comes from the fact that:

\sum_{k=0}^\infin \frac {1}{n^k}=1+\frac{1}{n-1} \quad\mbox{for all} \quad n\in\mathbb R > 1.

Powers of two are central to the concept of Mersenne primes, and important to computer science. In Mathematics, a power of two is any of the Integer powers of the number two; in other words two multiplied by itself a certain In Mathematics, a Mersenne number is a positive integer that is one less than a Power of two: M_n=2^n-1 Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their Two 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 two was the first known irrational number. The square root of 2, also known as Pythagoras' Constant, often denoted by \sqrt{2}   or   √2 In Mathematics, an irrational number is any Real number that is not a Rational number — that is it is a number which cannot be expressed as a fraction

The smallest field has two elements. In Abstract algebra, a field is an Algebraic structure in which the operations of Addition, Subtraction, Multiplication and division

In the set-theoretical construction of the natural numbers, 2 is identified with the set \{\{\emptyset\},\emptyset\}. This latter set is important in category theory: it is a subobject classifier in the category of sets. In Mathematics, category theory deals in an abstract way with mathematical Structures and relationships between them it abstracts from sets In Category theory, a subobject classifier is a special object &Omega of a category intuitively the Subobjects of an object X correspond to the morphisms

Two is a primorial, as well as its own factorial. The primorial has two similar but distinct meanings The name is attributed to Harvey Dubner and is a Portmanteau of prime and Factorial Definition The factorial function is formally defined by n!=\prod_{k=1}^n k Two often occurs in numerical sequences, such as the Fibonacci number sequence, but not quite as often as one does. In Mathematics, the Fibonacci numbers are a Sequence of numbers named after Leonardo of Pisa, known as Fibonacci 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. In Mathematics, a Motzkin number for a given number n (named after Theodore Motzkin) is the number of different ways of drawing non-intersecting chords In combinatorial Mathematics, the n th Bell number, named in honor of Eric Temple Bell, is the number of partitions of a set A Harshad number, or Niven number, is an Integer that is divisible by the sum of its digits in a given number base. In Mathematics, a meander or closed meander is a self-avoiding Closed curve which intersects a line a number of times In Mathematics, a meander or closed meander is a self-avoiding Closed curve which intersects a line a number of times In Mathematics, a meander or closed meander is a self-avoiding Closed curve which intersects a line a number of times

Two is the number of n-Queens Problem solutions for n = 4. The eight queens puzzle is the problem of putting eight Chess queens on an 8×8 chessboard such that none of them is able to capture any other using the standard chess With one exception, all known solutions to Znám's problem start with 2. In Number theory, Znám's problem asks which sets of k integers have the property that each integer in the set is a Proper divisor of the product of the

Two also has the unique property such that:

\sum_{k=0}^{n-1} 2^k = 2^{n} - 1

and also

\sum_{k=a}^{n-1} 2^k = 2^n - \sum_{k=0}^{a-1} 2^k - 1

for a not equal to zero

Two has a connection to triangular numbers:

\prod_{k=0}^n 2^k= 2^{tri_2(n)}

Where tri_d(n)= \frac {1}{d!}\prod_{k=0}^{d-1} (n+k)\quad \mbox{if}\quad d\ge 2 gives the nth d-dimensional simplex number. When d=2,

tri_2(n)=\frac {n^2+n}{2}

The number of domino tilings of a 2×2 checkerboard is 2. A checkerboard (or chequerboard) is a board on which American checkers is played

For any polyhedron homeomorphic to a sphere, the Euler characteristic is χ = V − E + F = 2. In Mathematics, and more specifically in Algebraic topology and Polyhedral combinatorics, the Euler characteristic is a Topological invariant

As of 2008, there are only two known Wieferich primes. In Number theory, a Wieferich prime is a Prime number p such that p 2 divides 2 p  &minus 1 &minus 1

List of basic calculations

Multiplication 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 50 100 1000
2 \times x 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 100 200 2000
Division 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
2 \div x 2 1 0.\overline{6} 0. In mathematics Four is the smallest Composite number, its proper Divisors being and. In mathematics Six is the second smallest Composite number, its proper Divisors being 1, 2 and 3. In mathematics 8 is a Composite number, its Proper divisors being 1, 2, and 4. 18 ( eighteen) is the Natural number following 17 and preceding 19. "Twenty" redirects here For the village in England, see Twenty Lincolnshire. 22 ( twenty-two) is the Natural number following 21 and preceding 23. 24 ( twenty-four) is the Natural number following 23 and preceding 25. 26 ( twenty-six) is the Natural number following 25 and preceding 27. 28 ( twenty-eight) is the Natural number following 27 and preceding 29. 30 ( thirty) is the Natural number following 29 and preceding 31. 32 ( thirty-two) is the Natural number following 31 and preceding 33. 34 ( thirty-four) is the Natural number following 33 and preceding 35. 36 ( thirty-six) is the Natural number following 35 and preceding 37. This article discusses the number thirty-eight. For the year 38 CE see 38. 40 ( forty) is the Natural number following 39 and preceding 41. 42 ( forty-two) is the Natural number following 41 and preceding 43. 44 ( forty-four) is the Natural number following 43 and preceding 45. 46 ( forty-six) is the Natural number following 45 and preceding 47. 48 ( forty-eight) is the Natural number following 47 and preceding 49. This article discusses the number fifty. For the year 50 CE see 50. 200 ( two hundred) is the Natural number following 199 and preceding 201. 2000 ( two thousand) is the Natural number following 1999 and preceding 2001 In Mathematics, especially in elementary Arithmetic, division is an arithmetic operation which is the inverse of Multiplication. 5 0. This article discusses the number five. For the year 5 AD see 5. 4 0.\overline{3} 0.\overline{2}8571\overline{4} 0. 25 0.\overline{2} 0. 25 ( twenty-five) is the Natural number following 24 and preceding 26. 2 0.\overline{1}\overline{8} 0.1\overline{6} 0.\overline{1}5384\overline{6} 0.\overline{1}4285\overline{7} 0.1\overline{3}
x \div 2 0. 5 1 1. 5 2 2. 5 3 3. 5 4 4. 5 5 5. 5 6 6. 5 7 7. In mathematics Seven is the fourth Prime number. It is not only a Mersenne prime (since 23 &minus 1 = 7 but also a 5
Exponentiation 1 2 3 4 5 6 7 8 9 10 11 12 13
2 ^ x\, 2 4 8 16 32 64 128 256 512 1024 2048 4096 8192
x ^ 2\, 1 4 9 16 25 36 49 64 81 100 121 144 169

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 Japanese). 64 ( sixty-four) is the Natural number following 63 and preceding 65. 256 (two hundred fifty-six CCLVI is the natural number following 255 and preceding 257. 500 ( five hundred) is the Natural number following 499 and preceding 501. In mathematics Nine is a Composite number, its proper Divisors being 1 and 3. This page is for the number For the steamboat see Forty-Nine (steamboat 49 ( forty-nine) is the Natural number following 48 81 ( eighty-one) is the Natural number following 80 and preceding 82. A glyph is an element of writing Two or more glyphs representing the same symbol whether interchangeable or context-dependent are called Allographs the abstract unit they Written Chinese comprises the written symbols used to represent Spoken Chinese and the rules about how they are arranged and punctuated The modern Japanese writing system uses three main scripts Kanji, characters of Chinese origin, Hiragana 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. The Gupta script (or Gupta Brahmi) was used for writing Sanskrit and is associated with the Gupta Empire of India which was a period of material 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. [2]

In fonts with text figures, 2 usually has the same height as a lowercase X, for example, Image:Text figures 256.svg. Text figures (also known as non-lining, lowercase, old-style, ranging or hanging figures or numerals are numerals

In science

Astronomy

In technology

2 as a resin identification code, used in recycling.

In religion

In culture

The twos of all four suits in playing cards
The twos of all four suits in playing cards


The most common philosophical dichotomy is perhaps the one of good and evil, but there are many others. A playing card is a piece of specially prepared heavy paper thin card or thin plastic figured with distinguishing motifs and used as one of a set for playing Card games A dichotomy is any splitting of a whole into exactly two non-overlapping parts Value theory encompasses a range of approaches to understanding how why and to what degree humans should or do value things whether the thing is a person idea object or anything else Evil, in many cultures is used to describe acts or thoughts which are contrary to some particular religion See dualism for an overview. Dualism denotes a state of two parts The word's origin is the Latin duo, "two". In Hegelian dialectic, the process of synthesis creates two perspectives from one. In classical Philosophy, dialectic (διαλεκτική is controversy the exchange of arguments and counter-arguments respectively advocating Propositions

Two (二, èr) is a good number in Chinese culture. In Chinese culture, certain numbers are believed by some to be auspicious (吉利 or inauspicious (不利 based on the Chinese word that the number name sounds similar to 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. Guangdong ( EFEO: Kouangtong; Pinyin Guǎngdōng; Postal map spelling: Kwangtung) is a province on the

In Finland, two candles are lit on Independence Day. Finland, officially the Republic of Finland ( is a Nordic country situated in the Fennoscandian region of northern Europe. A candle is a Light source and sometimes a Heat source consisting of a solid block of Fuel and an embedded wick. An Independence Day is an annual celebration commemorating the Anniversary of a Nation 's assumption of independent Statehood, usually after ceasing Putting them on the windowsill invokes the symbolical meaning of division, and thus independence.

In pre-1972 Indonesian and Malay orthography, 2 was shorthand for the reduplication that forms plurals: orang "person", orang-orang or orang2 "people". Indonesian or Bahasa Indonesia, based on the Riau version of Malay language, was declared the official language with the declaration of The Malay language ( ISO 639-1 code MS is an Austronesian language spoken by the Malay people and people of other ethnic groups who reside in the Reduplication, in Linguistics, is a morphological Process by which the root or stem of a Word, or part of it is repeated

In North American educational systems, the number 2. 00 denotes a grade-point average of "C," which in some colleges and universities is the minimum required for good academic standing at the undergraduate level. The following is a summary of the academic grading systems in North America. In some Educational systems undergraduate education is Post-secondary education up to the level of a Bachelor's degree. [4]

In Astrology, Taurus is the second sign of the Zodiac. Astrology (from Greek grc ἄστρον astron, "constellation star" and grc -λογία -logia) is a group of Systems Taurus (it looks like a bull (ˈtɔrəs bull, symbol, Unicode ♉ is one of the Constellations of the Zodiac. Astrological signs represent twelve equal segments or divisions of the Zodiac. Zodiac denotes an annual cycle of twelve stations along the Ecliptic, the apparent path of the sun across the heavens through the Constellations that divide the ecliptic

In other fields

International maritime pennant for 2 International maritime pennant for 2
International maritime pennant for 2
International maritime signal flag for 2

Groups of two:

References

  1. ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 41–44
  2. ^ Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer transl. David Bellos et al. London: The Harvill Press (1998): 393, Fig. 24. 62
  3. ^ Xavier Borg, Engineer (February 2, 2006). Magic numbers derived from VPM nuclear model. Blaze Labs Research. Retrieved on 2007-03-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1401 - Mongol emperor Timur sacks Damascus. 1603 - James VI of Scotland
  4. ^ For a typical example, see the University of Oklahoma grading regulations.
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