2 ( two; ) is a number, numeral system, and glyph. It is the natural number following 1 and preceding 3.
Two is the smallest and first prime number, and the only even prime number (for this reason it is sometimes called "the oddest prime").John Horton Conway & Richard K. Guy, The Book of Numbers. New York: Springer (1996): 25. . "Two is celebrated as the only even prime, which in some sense makes it the oddest prime of all." 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, the first Ramanujan prime, and the first Smarandache–Wellin prime.
Two is the third Fibonacci number.
Two is the radix of the binary system, the simplest numeral system in which natural numbers can be written concisely, which is used widely in Computer.
For any number x:
In general:
Two also has the unique property that , and so on, no matter how high the level of the hyperoperation is.
Two is the only number x such that the sum of the reciprocals of the powers of x equals itself. In symbols
This comes from the fact that:
Powers of two are central to the concept of , 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 2 was the first known irrational number.
The smallest field has two elements.
In the set theory 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 also has the unique property such that
and also
In ndimensional space for any n, any two distinct points determine a line.
For any polyhedron homeomorphic to a sphere, the Euler characteristic is , where V is the number of vertices, E is the number of edges, and F is the number of faces.
2 × 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 
2 ÷ x  2  1  0.  one half  0.4  0.  0.  0.25  0.  0.2  0.  0.1  0.  0.  0.1 
x ÷ 2  0.5  1  1.5  2  2.5  3  3.5  4  4.5  5  5.5  6  6.5  7  7.5 
2  2  4  8  16  32  64  128  256  512  1024  2048  4096  8192  16384  32768  65536  131072  262144  524288  1048576 
x  1  4  9  16  25  36  49  64  81  100  121  144  169  196  225  256  289  324  361  400 
In fonts with text figures, 2 usually is of xheight, for example, .
In Halakha, the testimonies of two witnesses are required to verify and validate events, such as marriage, divorce, and a crime that warrants capital punishment.
"SecondDay Yom Tov" ( Yom Tov Sheini Shebegaliyot) is a rabbinical enactment that mandates a twoday celebration for each of the oneday Jewish holiday (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.
The ancient Sanskrit language of India, does not only have a singular number and plural form for , as do many other languages, but instead has, a singular (1) form, a dual (2) form, and a plural (everything above 2) form, for all nouns, due to the significance of 2. It is viewed as important because of the anatomical significance of 2 (2 hands, 2 nostrils, 2 eyes, 2 legs, etc.)
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 brand names, e.g. double happiness, double coin, double elephants etc. Guangdong people like the number two because it sounds the same as the word "easy" (易) in Cantonese.
In Finland, two are lit on Independence Day and put on a windowsill, to remind passersby of the sacrifices of past generations in the struggle for independence and democracy.
In pre1972 Indonesian and Malay language orthography, 2 was shorthand for the reduplication that forms plurals: orang "person", orangorang or orang2 "people".
In Astrology, Taurus is the second sign of the Zodiac.
