Crossword clues for factorial
The Collaborative International Dictionary
Factorial \Fac*to"ri*al\, a.
Of or pertaining to a factory.
--Buchanan.(Math.) Related to factorials.
Factorial \Fac*to"ri*al\, n. (Math.)
pl. A name given to the factors of a continued product when the former are derivable from one and the same function F(x) by successively imparting a constant increment or decrement h to the independent variable. Thus the product F(x).F(x + h).F(x + 2h) . . . F[x + (n-1)h] is called a factorial term, and its several factors take the name of factorials.
--Brande & C.The product of the consecutive whole numbers from unity up to any given number; thus, 5 factorial is the product of 5 times four times three times two times one, or 120.
Douglas Harper's Etymology Dictionary
Wiktionary
a. 1 (context mathematics English) Of or pertaining to a factor or factorial#Noun. 2 Of or pertaining to a factor. 3 (context dated English) Of or pertaining to a factory. n. (context mathematics combinatorics English) The result of multiplying a given number of consecutive integers from 1 to the given number. In equations, it is symbolized by an exclamation mark (!). For example, 5! = 1 * 2 * 3 * 4 * 5 = 120.
WordNet
adj. of or relating to factorials
n. the product of all the integers up to and including a given integer; "1, 2, 6, 24, and 120 are factorials"
Wikipedia
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In mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example,
$$5! = 5 \times 4 \times 3 \times 2 \times 1 = 120. \$$
The value of 0! is 1, according to the convention for an empty product.
The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic occurrence is the fact that there are n! ways to arrange n distinct objects into a sequence (i.e., permutations of the set of objects). This fact was known at least as early as the 12th century, to Indian scholars. Fabian Stedman, in 1677, described factorials as applied to change ringing. After describing a recursive approach, Stedman gives a statement of a factorial (using the language of the original):
Now the nature of these methods is such, that the changes on one number comprehends [includes] the changes on all lesser numbers, ... insomuch that a compleat Peal of changes on one number seemeth to be formed by uniting of the compleat Peals on all lesser numbers into one entire body;
The notation n! was introduced by Christian Kramp in 1808.
The definition of the factorial function can also be extended to non-integer arguments, while retaining its most important properties; this involves more advanced mathematics, notably techniques from mathematical analysis.
Usage examples of "factorial".
Many factorial families had their own records of the Collapse, and the journals of the Eryx County Greggs were particularly detailed.
Since there are something like ten to the twentieth power-that is, a one with twenty zeroes after it-such neuroproteins in the brain, the number of possible combinations are of the order of factorial ten to, the twentieth power.
Since there are something like ten to the twentieth power--that is, a one with twenty zeros after it--such neuroproteins in the brain, the number of possible combinations are of the order of factorial ten to the twentieth power.
Since there are something like ten to the twentieth power - that is, a one with twenty zeros after it - such neuroproteins in the brain, the number of possible combinations are of the order of factorial ten to the twentieth power.
But she did understand that they were doing factorial trials, altering the conditions in each pedon and tracking what happened.