fatoriais

Fatorial is a mathematical operation denoted by an exclamation mark (!). The factorial of a non-negative integer n, symbolized as n!, is the product of all positive integers less than or equal to n. For example, 5! = 5 * 4 * 3 * 2 * 1 = 120.

By definition, the factorial of 0 is 1 (0! = 1). This definition is crucial for various mathematical formulas, particularly in combinatorics and calculus. The factorial function grows very rapidly; for instance, 10! is already 3,628,800.

Factorials are fundamental in calculating permutations and combinations. The number of ways to arrange n distinct items is n!. The number of ways to choose k items from a set of n items (combination) is given by the binomial coefficient, often expressed using factorials as n! / (k! * (n-k)!).

The factorial function is not defined for negative integers. While typically defined for integers, the Gamma function is a generalization of the factorial function that can accept complex numbers as arguments. The Gamma function is denoted by Γ(z) and is related to the factorial by Γ(n+1) = n! for non-negative integers n.