💯 Definition of Factorials, An Ultimate Guide
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Factorial is a mathematical concept representing the product of all positive integers less than or equal to n, where n is a non-negative integer. It's denoted by n!. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
A factorial can be defined as the product of all positive integers less than or equal to a given positive integer n. It's a mathematical operation that is widely used in various fields, such as combinatorics, probability, and statistics. Factorials have the following properties:
n! = n x (n-1)! for all positive integers n greater than 1.
0! is defined to be 1.
The factorial function is strictly increasing and thus has an inverse.
n! grows very quickly with n, for example, 20! = 2432902008176640000.
Factorials are often used to count the number of ways to arrange elements in a set or find combinations of elements. They also appear in Taylor series expansions and are used in calculus and mathematical analysis.
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