Faktorialeja

Faktorialeja is a term used in mathematics to refer to factorials. A factorial is the product of all positive integers up to a given non-negative integer. It is denoted by an exclamation mark (!). For example, the factorial of 5, written as 5!, is calculated as 5 × 4 × 3 × 2 × 1 = 120.

The factorial of 0 is defined as 1, which is an important convention in mathematics. Factorials grow very rapidly. For instance, 10! is 3,628,800, and 20! is a very large number. Factorials are fundamental in combinatorics, particularly in calculating permutations and combinations. They appear in many formulas in probability, algebra, and calculus.

The concept of factorial is primarily encountered in discrete mathematics and computer science. It is often used in algorithms related to sorting and searching. While the basic definition applies to non-negative integers, the concept can be extended to other mathematical domains through the Gamma function. The Gamma function, denoted by Γ(z), is a generalization of the factorial function to complex and real numbers. For positive integers n, Γ(n) = (n-1)!.

The calculation of factorials can quickly lead to very large numbers, which can exceed the capacity of standard data types in computer programming. This necessitates the use of special libraries or techniques for handling arbitrary-precision arithmetic when dealing with large factorials.