Faktöriyeller

Faktöriyeller, often referred to as factorials in English, represent a fundamental mathematical operation. 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 crucial for many mathematical formulas and combinatorial identities.

Factorials are extensively used in various branches of mathematics, particularly in combinatorics and probability theory. They are essential for calculating permutations, which represent the number of ways to arrange a set of objects, and combinations, which represent the number of ways to choose a subset of objects from a larger set. For instance, the number of ways to arrange n distinct objects is n!. The factorial function grows very rapidly; even relatively small values of n result in very large factorial numbers. This rapid growth makes factorials important in areas like the analysis of algorithms and the study of Stirling's approximation for large n.