Factorial of negative number

Is it possible to find factorial of negative numbers?

By definition,
N! = 1 x 2 x .... x N
⇒ N! = 1 x 2 x .... x N x (N+1) / (N+1)
⇒ N! = (N+1)! / (N+!)

Now, let's try some values:
3! = 4! / 4 = 6
2! = 3! / 3 = 2
1! = 2! / 2 = 1
0! = 1! / 1 = 1

So, that's how 0! = 1. Let's not stop at 0!, if we continue this fashion, we get:
(-1)! = 0! / 0 = Undetermined

Many people still keeps arguing about whether x / 0 = +∞ or Undefined, it really doesn't matter though, because it is well established that anything divided by zero is undefined.

However, in this post, we are going to talk about a problem from UVa Online Judge, UVa-10323 (Factorial! You Must be Kidding!!!). This problem actually requires you to calculate even the factorials of negative numbers, which does not really exist in real world.

In this context, we are forced to assume that x / 0 = +∞. There was a mistake on my previous post, this section is updated as per the comment from a fellow reader আহনাফ তাহমিদ:
(-1)! = 0! / 0 = +∞
(-2)! = (-1)! / -1 = -∞
(-3)! = (-2)! / -2 = +∞
(-4)! = (-3)! / -3 = -∞
(-5)! = (-4)! / -4 = +∞
and so on..

Hence, we can see that, if N is odd, then (-N)! = +∞, otherwise (-N)! = -∞. Note that, this specific problem statement calls +∞ as Overflow and -∞ as Underflow.

Hope it helps!