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In mathematics, the factorial of a positive integer n, denoted n!, Is the product of all positive integers less than or equal to n. For example,
5! = 1 x 2 x 3 x 4 x 5 = 120

0! is a special case, explicitly defined as 1.

The Factorial operation is found in many areas of mathematics, especially in combination algebra and mathematical analysis. His appearance is the most fundamental fact that there are n! ways of arranging n different objects in a sequence (for example, the permutations of a set of objects). This fact was at least as early 12 th century, Hindu-known scholars. The notation n! was introduced by Christian Kramp in 1808.

The definition of the factorial function can also be extended to non-integer arguments, while its main characteristics, the more advanced mathematics, including mathematical analysis techniques means.

Although the factorial function has its roots in the faculties which are combinatorial formulas in many areas of mathematics.

• There are n! different ways to arrange n different objects in a certain order, the permutations of these objects.
• Factor occur in algebra for various reasons, such as through the binomial coefficients given in the proposition, or an average of more permutations of symmetry of certain transactions.
• Factor in the calculation, for example, they occur in the denominators of the terms of the Taylor formula, especially to compensate for the fact that the nth derivative is n xn!.
• Factor are also widely used in probability theory.