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Что (кто) такое hereditarily factorial - определение
EXPERIMENT WHOSE DESIGN CONSISTS OF TWO OR MORE FACTORS, EACH WITH DISCRETE POSSIBLE VALUES, AND WHOSE EXPERIMENTAL UNITS TAKE ON ALL POSSIBLE COMBINATIONS OF THESE LEVELS ACROSS ALL SUCH FACTORS
Factorial experiments; Factorial design; Fully-crossed design; Fully crossed design; Factorial designs; Factorial trial
![Pareto plot]] showing the relative magnitude of the factor coefficients.](https://commons.wikimedia.org/wiki/Special:FilePath/Pareto plot filtration rate.svg?width=200 "Pareto plot]] showing the relative magnitude of the factor coefficients.")
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Factorial
![[[Relative error]] in a truncated Stirling series vs. number of terms](https://commons.wikimedia.org/wiki/Special:FilePath/Stirling series relative error.svg?width=200 "[[Relative error]] in a truncated Stirling series vs. number of terms")
![TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)](https://commons.wikimedia.org/wiki/Special:FilePath/Vintage Texas Instruments Model SR-50A Handheld LED Electronic Calculator, Made in the USA, Price Was $109.50 in 1975 (8715012843).jpg?width=200 "TI SR-50A]], a 1975 calculator with a factorial key (third row, center right)")
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
In mathematics, the factorial of a non-negative denoted is the product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial:
factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
<mathematics> The mathematical function that takes a
natural number, N, and returns the product of N and all
smaller positive integers. This is written
N! = N * (N-1) * (N-2) * ... * 1.
The factorial of zero is one because it is an {empty
product}.
Factorial can be defined recursively as
0! = 1
N! = N * (N-1)! , N > 0
The gamma function is the equivalent for real numbers.
(2005-01-07)
Factorial
PRODUCT OF ALL INTEGERS BETWEEN 1 AND THE INTEGRAL INPUT OF THE FUNCTION
Factorial function; Factorials; Superduperfactorial; N!; Factorial number; Factoral; Factorial growth; X!; ! (math); Approximations of factorial; Negative factorial
·adj Related to factorials.
II. Factorial ·adj Of or pertaining to a factory.
III. Factorial ·noun The product of the consecutive numbers from unity up to any given number.
IV. Factorial ·noun 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.
Factorial experiment
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design.
Factorial number system
![The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.](https://commons.wikimedia.org/wiki/Special:FilePath/Symmetric group 4; permutohedron 3D; Lehmer codes.svg?width=200 "The factorial numbers of a given length form a [[permutohedron]] when ordered by the bitwise <math>\le</math> relation<br/><br/>These are the right inversion counts (aka Lehmer codes) of the permutations of four elements.")
MIXED RADIX NUMERAL SYSTEM ADAPTED TO NUMBERING PERMUTATIONS; REPRESENTS A NUMBER AS A×0! + B×1! + C×2! + ⋯
Factoradix; Factorial base; Factoradic
In combinatorics, the factorial number system, also called factoradic, is a mixed radix numeral system adapted to numbering permutations. It is also called factorial base, although factorials do not function as base, but as place value of digits.
Bhargava factorial
GENERALIZATION OF THE MATHEMATICAL FACTORIAL
Bhargava's factorial function; Bhargava factorial function; Generalised factorial; Generalized factorial
In mathematics, Bhargava's factorial function, or simply Bhargava factorial, is a certain generalization of the factorial function developed by the Fields Medal winning mathematician Manjul Bhargava as part of his thesis in Harvard University in 1996. The Bhargava factorial has the property that many number-theoretic results involving the ordinary factorials remain true even when the factorials are replaced by the Bhargava factorials.
Factorial moment
EXPECTATION OR AVERAGE OF THE FALLING FACTORIAL OF A RANDOM VARIABLE
Normalised factorial moment; Factorial moments
In probability theory, the factorial moment is a mathematical quantity defined as the expectation or average of the falling factorial of a random variable. Factorial moments are useful for studying non-negative integer-valued random variables,D.
Fibonorial
MATHEMATICAL SERIES, PORTMANTEAU OF "FIBONACCI" AND "FACTORIAL"
Fibonacci factorial
In mathematics, the Fibonorial , also called the Fibonacci factorial, where is a nonnegative integer, is defined as the product of the first positive Fibonacci numbers, i.e.
Falling and rising factorials
MATHEMATICAL FUNCTIONS
Falling factorial; Rising factorial; Lower factorial; Upper factorial; Pockhammer symbol; Raising factorial; Pochhammer notation; Product of four consecutive integer; Falling Factorial Power; Falling factorial power; Pochammer symbol; Ascending factorial; Descending factorial; Factorial polynomial; Pochhammer function; Rising factorial power; Falling power; Factorial power; Pochhammer symbol; Rising power
In mathematics, the falling factorial (sometimes called the descending factorial, falling sequential product, or lower factorial) is defined as the polynomial
Hereditarily countable set
Pure countable set; Hereditarily countable
In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets. This inductive definition is well-founded and can be expressed in the language of first-order set theory.
Википедия
Factorial experiment
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.
For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a 2×2 factorial design. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction is present.
If the number of combinations in a full factorial design is too high to be logistically feasible, a fractional factorial design may be done, in which some of the possible combinations (usually at least half) are omitted.
