AskDefine | Define two

Dictionary Definition

two adj : being one more than one; "he received two messages" [syn: 2, ii] n : the cardinal number that is the sum of one and one or a numeral representing this number [syn: 2, II, deuce]

User Contributed Dictionary

English

Etymology

twa, feminine of twegen (English twain), from , from .

Pronunciation

  • a UK , /tuː/, /tu:/
  • a US , /tu/, /tu/
  • Rhymes: -uː

Homophones

Cardinal number

two
  1. The cardinality of the set ; one plus one. This many: ••. Ordinal: second.
  2. Describing a set or group with two components.

Translations

one plus one
set or group with two components
  • Lithuanian: dvejeri, dvejerios

Noun

  1. The digit/figure 2.
    The number 2202 contains three twos.
  2. A two-dollar bill.
  3. A child aged two.
    This toy is suitable for the twos and threes.

Translations

digit or figure
  • Bosnian: dvojka
  • Chinese: (èr)
  • Croatian: dvojka
  • Czech: dvojka
  • Danish: total
  • Dutch: twee
  • Esperanto: du
  • Estonian: kaks
  • Faroese: tveytal
  • Finnish: kakkonen
  • French: deux or p
  • German: Zwei
  • Hebrew: שתיים
  • Hungarian: kettő
  • Interlingua: duo, duos p
  • Italian: due or p
  • Japanese: (, ni)
  • Lithuanian: dvejetas
  • Persian: (do)
  • Polish: dwójka
  • Portuguese: dois
  • Romanian: doi
  • Russian: двойка
  • Serbian:
    Cyrillic: двојка
    Roman: dvojka
  • Slovene: dvojka
  • Spanish: dos
  • Swedish: tvåa
  • Tok Pisin: tu
  • Ukrainian: двійка (dvíjka)
  • Welsh: dau, dwy
two-dollar bill

Derived terms

Extensive Definition

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

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 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.
It is the third Fibonacci number, and the third and fifth Perrin 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:
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.
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 square root of two 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 \. 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
and also
\sum_^ 2^k = 2^n - \sum_^ 2^k - 1
for a not equal to zero
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,
tri_2(n)=\frac
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.

Astronomy

In technology

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 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.
In Astrology, Taurus is the second sign of the Zodiac.

In other fields

Groups of two:

References

two in Old English (ca. 450-1100): 2 (getæl)
two in Arabic: 2 (عدد)
two in Official Aramaic (700-300 BCE): 2 (ܡܢܝܢܐ)
two in Asturian: Dos
two in Guarani: Mokõi
two in Aymara: Paya
two in Catalan: Dos
two in Chuvash: 2 (хисеп)
two in Czech: 2 (číslo)
two in Corsican: 2 (numeru)
two in Danish: 2 (tal)
two in Pennsylvania German: Zwee
two in German: Zwei
two in Erzya: 2 (кавто)
two in Spanish: Dos
two in Esperanto: Du (nombro)
two in Basque: Bi
two in Persian: ۲ (عدد)
two in French: 2 (nombre)
two in Gan Chinese: 2
two in Korean: 2
two in Igbo: Abụo
two in Indonesian: 2 (angka)
two in Interlingua (International Auxiliary Language Association): 2 (numero)
two in Italian: 2 (numero)
two in Hebrew: 2 (מספר)
two in Kinyarwanda: Kabiri
two in Haitian: 2 (nonm)
two in Kurdish: Du
two in Latin: Duo
two in Luxembourgish: Zwee
two in Lithuanian: 2 (skaičius)
two in Latvian: 2 (skaitlis)
two in Lombard: Nümar 2
two in Hungarian: 2 (szám)
nah:Ōme
two in Dutch: 2 (getal)
two in Dutch Low Saxon: 2 (getal)
two in Japanese: 2
two in Neapolitan: Ddoje
two in Norwegian: 2 (tall)
two in Norwegian Nynorsk: Talet 2
two in Polish: 2 (liczba)
two in Portuguese: Dois
two in Quechua: Iskay
two in Russian: 2 (число)
two in Sicilian: Dui
two in Simple English: Two
two in Slovenian: 2 (število)
two in Serbian: 2 (број)
two in Finnish: 2 (luku)
two in Swedish: 2 (tal)
two in Tagalog: 2 (bilang)
two in Telugu: రెండు
two in Thai: 2
two in Vietnamese: 2 (số)
two in Turkish: 2 (sayı)
two in Buginese: 2 (nomoro)
two in Ukrainian: 2 (число)
two in Vlaams: 2 (getal)
two in Yiddish: 2 (נומער)
two in Contenese: 2
two in Chinese: 2

Synonyms, Antonyms and Related Words

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