factorial (Meaning)
factorial (n)
the product of all the integers up to and including a given integer
factorial (a)
of or relating to factorials
factorial (a.)
Of or pertaining to a factory.
Related to factorials.
factorial (n.)
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.
The product of the consecutive numbers from unity up to any given number.
Synonyms & Antonyms of factorial
No Synonyms and anytonyms found
factorial Sentence Examples
- The factorial of 5, denoted as 5!, is calculated by multiplying all positive integers less than or equal to 5, resulting in The factorial function possesses the unique property that the factorial of any non-negative integer n can be defined recursively as n!
- = n * (n-1)!.
- Factorials are often encountered in many branches of mathematics, including combinatorics, probability theory, and calculus.
- In combinatorics, factorials are used to determine the number of ways to arrange a set of objects in a particular order.
- The factorial of a large number can be efficiently computed using a logarithmic function, avoiding the need for explicit multiplication.
- The factorial function exhibits a rapid increase as the input value increases, making it useful for exploring concepts such as infinity and limits.
- The factorial of a negative integer is not defined, as the multiplication of negative integers leads to undefined results.
- The double factorial, denoted as n!
- !, is defined as the product of all positive integers less than or equal to n that have the same parity as n. Factorials find applications in various fields, such as physics, statistics, and computer science, where they are used to model various phenomena and solve complex problems.
- The factorial of a complex number can be defined using the gamma function, which extends the concept of factorials to non-integer values.
FAQs About the word factorial
the product of all the integers up to and including a given integer, of or relating to factorialsOf or pertaining to a factory., Related to factorials., A name
No synonyms found.
No antonyms found.
The factorial of 5, denoted as 5!, is calculated by multiplying all positive integers less than or equal to 5, resulting in The factorial function possesses the unique property that the factorial of any non-negative integer n can be defined recursively as n!
= n * (n-1)!.
Factorials are often encountered in many branches of mathematics, including combinatorics, probability theory, and calculus.
In combinatorics, factorials are used to determine the number of ways to arrange a set of objects in a particular order.
