both adj : (used with count nouns) two considered together; the two; "both girls are pretty" [syn: both(a)]
EtymologyVia from báðir.
- Each of the two; one and the other.
- "Did you want this one or that one?" "Give me both."
- Both children are such dolls.
- "Did you want this one or that one?" "Give me both."
each of two; one and the other
- Bosnian: oba
- Chinese: 双方
- Croatian: oba
- Dutch: beide, allebei, allebeide, alletwee
- Esperanto: ambaŭ
- Finnish: molemmat p, kumpikin s
- French: les deux, ambedeux (unused)
- German: beide
- Hebrew: שנינו (shneinu) m|p, שתינו (shteinu) f|p - both of us; שניכם (shneikhem) m|p, שתיכן (shteikhen) f|p - both of you; שניהם (shneihem) m|p, שתיהן (shteihen) f|p - both of them
- Icelandic: bæði; báðir m|p, báðar f|p, bæði n p
- Ido: ambe
- Indonesian: keduanya
- Interlingua: ambe
- Italian: entrambi, tutti e due , tutte le due , ambedue
- Japanese: 両方 (りょうほう, ryōhō), 両-
- Polish: oboje (animate), obie (non-animate)
- Portuguese: ambos
- Romanian: ambii , ambele
- Russian: оба m|n, обе
- Scots: baith
- Slovene: oba , obe
- Spanish: ambos
- Swedish: båda, bägge
- Telugu: రెండూ, ఇద్దరూ (reMDoo, iddaroo)
- West Frisian: beide, allebeide
EtymologyFrom both < (cf. Middle Welsh bot) < .
In mathematicsTwo 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 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"). 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.
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.
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.
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.
For any number x:
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.
Two is the only number x such that the sum of the reciprocals of the powers of x equals itself. In symbols: \sum_^\frac =1+\frac+\frac+\frac+\frac+\cdots=2.
This comes from the fact that: \sum_^\infin \frac =1+\frac \quad\mbox \quad n\in\mathbb 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.
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 smallest field has two elements.
In the 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 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.
Two also has the unique property such that:
- \sum_^ 2^k = 2^ - 1
- \sum_^ 2^k = 2^n - \sum_^ 2^k - 1
Two has a connection to triangular numbers:
\prod_^n 2^k= 2^
Where tri_d(n)= \frac \prod_^ (n+k)\quad \mbox\quad d\ge 2 gives the nth d-dimensional simplex number. When d=2,
The number of domino tilings of a 2×2 checkerboard is 2.
For any polyhedron homeomorphic to a sphere, the Euler characteristic is \chi = V-E+F = 2.
As of 2008, there are only two known Wieferich primes.
List of basic calculations
Evolution of the 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 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.
In fonts with text figures, 2 usually has the same height as a lowercase X, for example, *The number of polynucleotide strands in a DNA double helix.
- Messier object M2, a magnitude 6.5 globular cluster in the constellation Aquarius.
- The New General Catalogue object NGC 2, a magnitude 14.2 spiral galaxy in the constellation Pegasus
- The Saros number of the solar eclipse series which began on May 4 2861 BC and ended on June 21 1563 BC . The duration of Saros series 2 was 1298.1 years, and it contained 73 solar eclipses.
- The Saros number of the lunar eclipse series which began on February 21 2541 BC and ended on April 22 1225 BC. The duration of Saros series 2 was 1316.2 years, and it contained 74 lunar eclipses.
- The Roman numeral II stands for bright giant in the Yerkes spectral classification scheme.
- The Roman numeral II (usually) stands for the second-discovered satellite of a planet or minor planet (e.g. Pluto II or (87) Sylvia II Remus)
- A binary star is a stellar system consisting of two stars orbiting around their center of mass.
- 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.
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.
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 pre-1972 Indonesian and Malay orthography, 2 was shorthand for the reduplication that forms plurals: orang "person", orang-orang or orang2 "people".
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 name of several fictional characters: Number Two.
- The designation of the Trans-Canada Highway in most of the province of New Brunswick.
- U.S. Route 2, two separated highways in the northern tier of the United States, the western segment connecting Everett, Washington to St. Ignace, Michigan and the eastern route connecting Rouses Point, New York to Houlton, Maine.
- The lowest channel of television in the United States, Canada, and Mexico on which television signals are broadcast.
both in Old English (ca. 450-1100): 2 (getæl)
both in Arabic: 2 (عدد)
both in Official Aramaic (700-300 BCE): 2 (ܡܢܝܢܐ)
both in Asturian: Dos
both in Guarani: Mokõi
both in Aymara: Paya
both in Catalan: Dos
both in Chuvash: 2 (хисеп)
both in Czech: 2 (číslo)
both in Corsican: 2 (numeru)
both in Danish: 2 (tal)
both in Pennsylvania German: Zwee
both in German: Zwei
both in Erzya: 2 (кавто)
both in Spanish: Dos
both in Esperanto: Du (nombro)
both in Basque: Bi
both in Persian: ۲ (عدد)
both in French: 2 (nombre)
both in Gan Chinese: 2
both in Korean: 2
both in Igbo: Abụo
both in Indonesian: 2 (angka)
both in Interlingua (International Auxiliary Language Association): 2 (numero)
both in Italian: 2 (numero)
both in Hebrew: 2 (מספר)
both in Kinyarwanda: Kabiri
both in Haitian: 2 (nonm)
both in Kurdish: Du
both in Latin: Duo
both in Luxembourgish: Zwee
both in Lithuanian: 2 (skaičius)
both in Latvian: 2 (skaitlis)
both in Lombard: Nümar 2
both in Hungarian: 2 (szám)nah:Ōme
both in Dutch: 2 (getal)
both in Dutch Low Saxon: 2 (getal)
both in Japanese: 2
both in Neapolitan: Ddoje
both in Norwegian: 2 (tall)
both in Norwegian Nynorsk: Talet 2
both in Polish: 2 (liczba)
both in Portuguese: Dois
both in Quechua: Iskay
both in Russian: 2 (число)
both in Sicilian: Dui
both in Simple English: Two
both in Slovenian: 2 (število)
both in Serbian: 2 (број)
both in Finnish: 2 (luku)
both in Swedish: 2 (tal)
both in Tagalog: 2 (bilang)
both in Telugu: రెండు
both in Thai: 2
both in Vietnamese: 2 (số)
both in Turkish: 2 (sayı)
both in Buginese: 2 (nomoro)
both in Ukrainian: 2 (число)
both in Vlaams: 2 (getal)
both in Yiddish: 2 (נומער)
both in Contenese: 2
both in Chinese: 2