104 articles
9 (number)
9 (nine) is the natural number following 8 and preceding 10: the largest single digit, the square of 3, and the smallest odd composite number, basis of casting out nines.
90 (number)
90 (ninety), the natural number following 89 and preceding 91, is an abundant pronic number with twelve divisors, best known as the degree measure of a right angle.
Abundant number
An abundant number, or excessive number, is a positive integer whose proper divisors add up to more than the number itself, the smallest being 12.
Almost integer
An almost integer is a real number very close to, but not equal to, an integer. The flagship example, e^(π√163), differs from 262537412640768744 by less than 10^-12.
Amicable numbers
Amicable numbers, or amicable pairs, are two numbers each equal to the sum of the other's proper divisors; the smallest pair, 220 and 284, was known to Thābit ibn Qurra in the ninth century.
Bell number
The Bell number B(n) is the number of ways to partition a set of n labeled elements into non-empty subsets; the sequence begins 1, 1, 2, 5, 15.
Billion
Billion, also called one billion, is the number 1,000,000,000 (a thousand million) in American and British English, though older European usage gives it the value 10^12.
Catalan number
The Catalan numbers, also called the Catalan sequence, form an integer sequence beginning 1, 1, 2, 5, 14, 42 that counts balanced parentheses and triangulations.
Cube (algebra)
The cube of a number, or cubic number, is the number multiplied by itself twice, written a3; cubing gives the volume of a cube with edge a.
Cyclic number
A cyclic number is an integer whose multiples are cyclic permutations of its own digits; 142857, the repeating decimal block of 1/7, is the classic example.
Digital root
The digital root, also called the repeated digital sum, is the single digit left after repeatedly summing an integer's digits; it equals the remainder modulo 9.
Double factorial
The double factorial of a nonnegative integer n, written n!!, is the product of all positive integers up to n with the same parity as n.
Fermat number
A Fermat number is an integer of the form 2^(2^n) + 1, named after Pierre de Fermat. Only the first five, 3 through 65537, are known to be prime.
Gelfond's constant
Gelfond's constant is the transcendental number e^π, approximately 23.1407, proven transcendental in 1934 by Aleksandr Gelfond and independently by Theodor Schneider in 1935, settling Hilbert's seventh problem.
Googol
A googol, ten duotrigintillion, is the number 10 to the 100th power, named in 1938 by nine-year-old Milton Sirotta, whose uncle Edward Kasner popularized it.
Graham's number
Graham's number is an enormous integer, built from Knuth's up-arrow notation, that arose as a Ramsey theory upper bound and was popularized by Martin Gardner in 1977.
Happy number
A happy number is a positive integer that reaches 1 when repeatedly replaced by the sum of the squares of its digits, for example 7, 13, and 19.
Highly composite number
A highly composite number, also called an anti-prime or maximally divisible number, is a positive integer with more divisors than any smaller one, first analyzed by Ramanujan in 1915.
Kaprekar number
A Kaprekar number is a positive integer whose square can be split into two parts that add up to the original number, such as 45.
Lakh (लाख)
Lakh (लाख), also spelled lac, is a unit in the Indian numbering system equal to one hundred thousand, the standard large-number word in South Asian finance and everyday speech.
Large numbers
Large numbers, or very large numbers, are numbers far beyond everyday counting, conventionally starting around a million, expressed through -illion names, scientific notation, SI prefixes, and googology.
Long and short scales
The long and short scales are two competing systems for naming large numbers: in the short scale each new term is 1,000 times the previous one, in the long scale 1,000,000 times.
Myriad
A myriad is, precisely, the number ten thousand, the largest number named by one word in ancient Greek; in modern English it loosely means an indefinitely great number.
Names for the number 0 in English
English has several names for the number 0: zero, the general term; oh for reading digits; nought in British use; nil for sports scores; and love in tennis.
Names of large numbers
Names of large numbers are the English words for powers of ten beyond a thousand, coined from Latin with the -illion ending, as in million, billion, and trillion.
Narayana number
The Narayana numbers, named for the Canadian mathematician T. V. Narayana, form a symmetric triangular array counting Dyck paths with k peaks; row sums give the Catalan numbers.
Narcissistic number
A narcissistic number, also called an Armstrong number, is a number equal to the sum of its digits each raised to the number of digits, like 153.
Number of the beast
The number of the beast, also called the beast number (Greek: Χξς), is 666, given in Revelation 13:18 as the number of a beastly figure who forces everyone to receive a mark.
Palindromic number
A palindromic number, also called a numeral palindrome, reads the same forwards and backwards in some base, such as 121 or 94200249 in decimal.
Perfect numbers
A perfect number is a positive integer equal to the sum of its proper divisors, such as 6 and 28; every even one arises from a Mersenne prime.