faktoriaalia

Faktoriaalia, often referred to as factorial in English, is a mathematical operation represented by an exclamation mark (!). It is defined for non-negative integers. The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n. For example, 5! equals 5 × 4 × 3 × 2 × 1, which results in 120.

By definition, the factorial of zero (0!) is equal to 1. This convention is important for various mathematical formulas, particularly in combinatorics and calculus. The factorial function grows very rapidly. For instance, 10! is already 3,628,800.

The concept of factorial is fundamental in many areas of mathematics. It appears in the formula for permutations and combinations, which are used to count the number of ways to arrange or select items from a set. Factorials are also crucial in the study of probability, as well as in the Taylor series expansions of functions in calculus. While traditionally defined for integers, the concept has been generalized to real and complex numbers through the Gamma function, though this is a more advanced topic.