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Factorials of negative integers are generally undefined in standard mathematics because the defining formula n!=n× (n-1)! leads to a division by zero (e.g., (-1)!=0!÷0. While the Gamma function, Gamma (n+1)=n!, extends factorials to complex numbers, it becomes infinite at negative integers. Some contexts, however, may define them using extended formulas, such as (-n)!=(-1)^{n}n!
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A factorial (denoted by !) is the product of all positive whole numbers less than or equal to a given number, calculated as n!=n× (n-1)×....× 2×1, used primarily in combinatorics to find permutations (arrangements) of items, with 0! is defined as 1. For example, 4! is
4×3 ×2 ×1 =24.
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