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Encyclopedia > 2 (number)
Look up two, both in Wiktionary, the free dictionary.

2 (two) is a number, numeral, and glyph. It is the natural number following 1 and preceding 3. Look up binary in Wiktionary, the free dictionary. ... The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. ... The duodecimal (also known as base-12 or dozenal) system is a numeral system using twelve as its base. ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0â€“9 and Aâ€“F, or aâ€“f. ... Wikipedia does not have an article with this exact name. ... Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 151 languages. ... Image File history File links No higher resolution available. ... For other uses, see Number (disambiguation). ... A numeral is a symbol or group of symbols that represents a number. ... variant glyphs representing the character a (allographs of a) in the Zapfino typeface. ... In mathematics, a natural number can mean either an element of the set {1, 2, 3, ...} (i. ... One redirects here. ... This article is about the number. ...

## Contents

Two has many properties in mathematics.[1] 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 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. For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Not to be confused with Natural number. ... Look up een, even in Wiktionary, the free dictionary. ... For other uses, see Decimal (disambiguation). ... In mathematics and computer science, hexadecimal, base-16, or simply hex, is a numeral system with a radix, or base, of 16, usually written using the symbols 0â€“9 and Aâ€“F, or aâ€“f. ...

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"). The next prime is three. 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. It is an Eisenstein prime with no imaginary part and real part of the form 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. In mathematics, a prime number (or a prime) is a natural number greater than 1 which has exactly two distinct natural number divisors: 1 and itself. ... This article is about the number. ... A prime number p is called a Sophie Germain prime if 2p + 1 is also prime. ... A factorial prime is a number that is one less or one more than a factorial and is also a prime number. ... A Lucas prime is a Lucas number that is prime. ... In mathematics, Smarandache-Wellin numbers are special integers; the n-th Smarandache-Wellin number is defined as the concatenation of the first n prime numbers written in decimal notation. ... An Eisenstein prime is an Eisenstein integer aÏ‰ + b that has only two Eisenstein divisors, the complex cube root of unity and aÏ‰ + b itself. ... A Stern prime 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. ... A Markov number or Markoff number is an integer x, y or z that is part of a solution to the Markov Diophantine equation The first few Markov numbers are 1, 2, 5, 13, 29, 34, 89, 169, 194, 233, 433, 610, 985, 1325, ... (sequence A002559 in OEIS) appearing in...

It is the third Fibonacci number, and the third and fifth Perrin numbers. A tiling with squares whose sides are successive Fibonacci numbers in length 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, and P(n) = P(n âˆ’ 2) + P(n âˆ’ 3) for n > 2. ...

Despite being a prime, two is also a highly composite number, because it has more divisors than the number one. The next highly composite number is four. A highly composite number is a positive integer which has more divisors than any positive integer below it. ... This article discusses the number Four. ...

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 arithmetic, a vulgar fraction (or common fraction) consists of one integer divided by a non-zero integer. ... A denominator is a name. ... It has been suggested that this article or section be merged with decimal. ... In mathematics, a divisor of an integer n, also called a factor of n, is an integer which evenly divides n without leaving a remainder. ... This article is about the number 10. ...

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. 3 + 2 = 5 with apples, a popular choice in textbooks[1] This article is about addition in mathematics. ... In mathematics, multiplication is an elementary arithmetic operation. ... In mathematics, multiplication is an elementary arithmetic operation. ... â€œExponentâ€ redirects here. ... â€œExponentâ€ redirects here. ... Tetration (also exponential map, hyperpower, power tower, super-exponentiation, and hyper4) is iterated exponentiation, the first hyper operator after exponentiation. ...

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:

$sum_{k=0}^infin frac {1}{n^k}=1+frac{1}{n-1} quadmbox{for all} quad ninmathbb R > 1.$

Powers of two are central to the concept of Mersenne primes, and important to computer science. Two is the first Mersenne prime exponent. In mathematics, a power of two is any of the nonnegative integer powers of the number two; in other words, two times itself a certain number of times. ... In mathematics, a Mersenne number is a number that is one less than a power of two. ... Computer science, or computing science, is the study of the theoretical foundations of information and computation and their implementation and application in computer systems. ...

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 two is the positive real number which, when multiplied by itself, gives a product of two. ... In mathematics, an irrational number is any real number that is not a rational number â€” that is, it is a number which cannot be expressed as a fraction m/n, where m and n are integers, with n non-zero. ...

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 (except division by zero) may be performed, and the same rules hold which are familiar from the arithmetic of ordinary numbers. ...

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. Set theory is the mathematical theory of sets, which represent collections of abstract objects. ... In mathematics, category theory deals in an abstract way with mathematical structures and relationships between them. ... In category theory, a subobject classifier is a special object Î© of a category; intuitively, the subobjects of an object X correspond to the morphisms from X to Î©. As the name suggests, what a subobject classifier does is to identify/classify subobjects of a given object according to which elements belong...

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. For n ≥ 2, the primorial n# is the product of all prime numbers less than or equal to n. ... For factorial rings in mathematics, see unique factorisation domain. ... In mathematics, the Fibonacci numbers form a sequence defined recursively by: In words: you start with 0 and 1, and then produce the next Fibonacci number by adding the two previous Fibonacci numbers. ... In mathematics, a Motzkin number for a given number n is the number of different ways of drawing non-intersecting chords on a circle between n points. ... The Bell numbers, named in honor of Eric Temple Bell, are a sequence of integers arising in combinatorics that begins thus (sequence A000110 in OEIS): In general, Bn is the number of partitions of a set of size n. ... 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. With one exception, all known solutions to Znám's problem start with 2. One solution. ... ZnÃ¡ms problem is the question of what sets of integers, of a given length, can be put together such that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. ...

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 $tri_d(n)= frac {1}{d!}prod_{k=0}^{d-1} (n+k)quad mbox{if}quad dge 2$ 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. 5 by 5 checkerboard pattern 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 = VE + F = 2. In algebraic topology, the Euler characteristic is a topological invariant, a number that describes one aspect of a topological spaces shape or structure. ...

As of 2008, there are only two known Wieferich primes. In mathematics, a Wieferich prime is prime number p such that pÂ² divides 2p âˆ’ 1 âˆ’ 1; compare this with Fermats little theorem, which states that every prime p divides 2p âˆ’ 1 âˆ’ 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 $0.overline{6}$ 0.5 0.4 $0.overline{3}$ $0.overline{2}8571overline{4}$ 0.25 $0.overline{2}$ 0.2 $0.overline{1}overline{8}$ $0.1overline{6}$ $0.overline{1}5384overline{6}$ $0.overline{1}4285overline{7}$ $0.1overline{3}$
$x div 2$ 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
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 File history File links Evolution of the numeral 2 from the Brahmin Indians to the Europeans I drew these characters by hand and scanned them. ...

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). 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.[2] variant glyphs representing the character a (allographs of a) in the Zapfino typeface. ... Various styles of Chinese calligraphy. ... The Gupta script was used for writing Sanskrit and is associated with the Gupta Empire of India which was a period of material prosperity and great religious and scientific developments. ... The Brahmic family is a family of abugidas used in South Asia and Southeast Asia. ...

In fonts with text figures, 2 usually has the same height as a lowercase X, for example, . Hoefler Text, a contemporary font, uses hanging or old style text figures. ... Image File history File links Text_figures_256. ...

## In technology

Sorted household plastic waiting to be hauled away for reprocessing. ... HDPE has SPI resin ID code 2 High-density polyethylene (HDPE) is a polyethylene thermoplastic made from petroleum. ...

## In religion

• The Ten Commandments were given in the form of two tablets (Shnei Luchot HaBrit)
• Two candles are traditionally kindled to usher in the Shabbat, recalling the two different ways Shabbat is referred to in the two times the Ten Commandments are recorded in the Torah. These two expressions are known in Hebrew as שמור וזכור ("guard" and "remember"), as in "Guard the Shabbat day to sanctify it" (Deut. 5:12) and "Remember the Shabbat day to sanctify it" (Ex. 20:8)
• Two challahs (lechem mishnah) are placed on the table for each Shabbat meal and a blessing made over them, to commemorate the double portion of manna which fell in the desert every Friday to cover that day's meals and the Shabbat meals
• In Jewish law, the testimony of two witnesses are required to verify and validate events, such as marriage, divorce, and a crime that warrants capital punishment
• Rosh Hashana, the first day of the Jewish year, is a 2-day holiday
• "Second-Day Yom Tov" (Yom Tov Sheini Shebegaliyot) is a rabbinical enactment that mandates a two-day celebration for each of the one-day Jewish festivals (i.e., the first and seventh day of Passover, the day of Shavuot, the first day of Sukkot, and the day of Shemini Atzeret) outside the land of Israel
• Animals boarded Noah's Ark two by two.

## In culture

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. See dualism for an overview. In Hegelian dialectic, the process of synthesis creates two perspectives from one. Set of 78 French style playing cards with twenty two atouts, typically used to play French Tarot Set of 52 French style playing cards with two jokers Set of 52 Anglo-American style playing cards Some typical Anglo-American playing cards from the Bicycle brand Paul CÃ©zanne - The Card... A dichotomy is a division into two non-overlapping or mutually exclusive and jointly exhaustive parts. ... This article or section is in need of attention from an expert on the subject. ... For other uses, see Evil (disambiguation). ... For other uses, see Dualism (disambiguation). ... Hegel redirects here. ... In classical philosophy, dialectic (Greek: Î´Î¹Î±Î»ÎµÎºÏ„Î¹ÎºÎ®) is controversy, Viz. ... Synthesis (from the ancient Greek ÏƒÏÎ½ (with) and Î¸ÎµÏƒÎ¹Ï‚ (placing), is commonly understood to be an integration of two or more pre-existing elements which results in a new creation. ...

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. Numbers in Chinese culture play a significant role based on the belief that certain numbers are lucky or unlucky. ... Not to be confused with the former Kwantung Leased Territory in north-eastern China. ... This article is on all of the Yue dialects. ...

In Finland, two candles are lit on Independence Day. Putting them on the windowsill invokes the symbolical meaning of division, and thus independence.[citation needed] For other uses, see Candle (disambiguation). ... For other uses, see Independence Day (disambiguation). ...

In pre-1972 Indonesian and Malay orthography, 2 was shorthand for the reduplication that forms plurals: orang "person", orang-orang or orang2 "people".[citation needed] Not to be confused with the Malayalam language, spoken in India. ... Reduplication, in linguistics, is a morphological process in which the root or stem of a word, or only 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.[4] The following is a summary of the Academic grading systems in the United States and Canada. ... In some educational systems, undergraduate education is post-secondary education up to the level of a Bachelors degree. ...

In Astrology, Taurus is the second sign of the Zodiac. Hand-coloured version of the anonymous Flammarion woodcut (1888). ... Taurus (IPA: , Latin: , symbol , ) is one of the constellations of the zodiac. ... Astrological represent twelve equal segments or divisions of the zodiac. ... For other uses, see Zodiac (disambiguation). ...

## In other fields

Groups of two: Image File history File links ICS_Pennant_Two. ... Image File history File links ICS_Two. ... The Commissioning pennant or Masthead pennant is a pennant (also spelt pendant) flown from the masthead of a warship. ... The system of international maritime signal flags is a way of representing individual letters of the alphabet on ships or in nautical situations. ...

This is a list of lists of pairs by category. ... For mythological and fictional twins, see Category:Fictional twins. ... A number of fictional characters have been called Number Two. // Number Two was the apparent second-in-command in the Village in the British television show The Prisoner. ... For the Boards of Canada record, see Trans Canada Highway (EP). ... This article is about the Canadian province. ... United States Highway 2 is an east-west United States Highway. ... County Snohomish Government  - Mayor Ray Stephanson Area  - City 123. ... Saint Ignace, usually written as St. ... Rouses Point is a village located in Clinton County, New York. ... Location of town of Houlton in state of Maine Houlton is a town in Aroostook County, Maine, on the United States-Canada border, located at . ...

## References

Wikimedia Commons has media related to:
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.
4. ^ For a typical example, see the University of Oklahoma grading regulations.
Year 2007 (MMVII) was a common year starting on Monday of the Gregorian calendar in the 21st century. ... is the 83rd day of the year (84th in leap years) in the Gregorian calendar. ...

Results from FactBites:

 What's Special About This Number? (7326 words) is the number of planar partitions of 10. is the number of planar partitions of 11. is the number of planar partitions of 12.
 2 (number) at AllExperts (1049 words) 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). 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 number 2 is sometimes used as a shorthand for "to".
More results at FactBites »

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