Moreover, they start getting the factorial of negative numbers, like $-\frac {1} {2}! = \sqrt {\pi}$ How is this possible? What is the definition of the factorial of a fraction? What about negative numbers? I tried …

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...

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 …

Is there any way I can 'undo' the factorial operation? JUst like you can do squares and square roots, can you do factorials and factorial roots (for lack of a better term)? Here is an example: 5!...

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 …

45 (Too long for a comment) I don't know if there's a simpler form, but the sum of factorials has certainly been well-studied. In the literature, it is referred to as either the left factorial (though this term is also …

Interestingly, if you continue summing the digits for any integer factorial larger than or equal to 6, such that you end with a single digit, the answer will always be 9.

He describes it precisely for the purpose of contrasting with the factorial function, and the name seems to be a play on words (term-inal rather than factor-ial).

In our algorithms class, my professor insists that n! has a higher order of growth than n^n. This doesn't make sense to me, when I work through what each expression means. n! = n * (n-1) * (n-2) ...

It is a valid question to extend the factorial, a function with natural numbers as argument, to larger domains, like real or complex numbers. The gamma function also showed up several times as …