# Dictionary Definition

both adj : (used with count nouns) two considered
together; the two; "both girls are pretty" [syn: both(a)]

# User Contributed Dictionary

## English

### Etymology

Via from báðir.### Determiner

- Each of the two; one and the other.
- "Did you want this one or that one?" "Give me both."
- Both children are such dolls.

#### Translations

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-
- Kurdish:
- Polish: oboje (animate), obie (non-animate)
- Portuguese: ambos
- Romanian: ambii , ambele
- Russian: оба m|n, обе
- Scots: baith
- Serbian:
- Slovene: oba , obe
- Spanish: ambos
- Swedish: båda, bägge
- Telugu: రెండూ, ఇద్దరూ (reMDoo, iddaroo)
- West Frisian: beide, allebeide

### Etymology

From both < (cf. Middle Welsh bot) < .### Pronunciation

- lang=ga|[bˠɔh]|[bˠɔ]

### Noun

#### Declension

#### Mutation

# Extensive Definition

## 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

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.

- The first magic number.
- The atomic number of helium.
- Group 2 in the Periodic table of the elements consists of the alkaline earth metals whose usual valence is +2.
- Period 2 in the Periodic table consists of the eight elements lithium through neon.

### Astronomy

- 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.

## In technology

- The resin identification code used in recycling to identify high-density polyethylene.

## 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 other fields

Groups of two:- 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.

## References

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