Nine

Nine is the natural number that comes after eight and before ten. In decimal notation it is written as 9 and in Roman numerals as IX. It is the largest single-digit number in common use.

In mathematics, 9 is a composite number with divisors 1, 3, and 9. It is the square of 3, making it a perfect square. It is odd and, in base-10 arithmetic, has a notable property: the sum of the digits of any multiple of 9 is itself a multiple of 9, and the digital root of such numbers is 9. It is also a Harshad number in base 10, meaning it is divisible by the sum of its digits.

Culturally, nine has various symbolic meanings. In Norse mythology, Yggdrasil, the world tree, is said to connect nine worlds, and Odin is told to have hung on the tree for nine nights to gain wisdom. The nine Muses occupy an important place in Greek myth as patronesses of the arts. In East Asian cultures, the number nine is sometimes associated with longevity and completeness, and may appear in imperial symbolism and celebrations. In everyday idioms, phrases such as “cloud nine” and “dressed to the nines” reflect its continued presence in language.

In arts and media, Nine has been used as a title for several works, including a 2009 film adaptation of the stage musical, which itself draws on Federico Fellini’s 8½. The word also appears in music, literature, and other media, where it is often chosen for its symbolic connotations or rhythmic qualities.