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complex analysis - Why is $i! = 0. 498015668 - 0. 154949828i . . . Why is this? I know what a factorial is, so what does it actually mean to take the factorial of a complex number? Also, are those parts of the complex answer rational or irrational? Do complex factorials give rise to any interesting geometric shapes curves on the complex plane?
What does the factorial of a negative number signify? So, basically, factorial gives us the arrangements Now, the question is why do we need to know the factorial of a negative number?, let's say -5 How can we imagine that there are -5 seats, and we need to arrange it? Something, which doesn't exist shouldn't have an arrangement right? Can someone please throw some light on it?
How do we calculate factorials for numbers with decimal places? I was playing with my calculator when I tried $1 5!$ It came out to be $1 32934038817$ Now my question is that isn't factorial for natural numbers only? Like $2!$ is $2\\times1$, but how do we e
factorial - Why does 0! = 1? - Mathematics Stack Exchange The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes