Eli5 why we cant have negative factorials?

Question

I looked it up on google but my extent of math goes to algebra 2, but it immediately went into wacky stuff like “the gamma function”, simply put, what is the gamma function and why is it stopping stuff like -9! From being -362880

In: 2

Answer 1

By (the basic) definition, for any number **n**, we define the factorial (**n!**) as **n***(**n**-1)*(**n**-2)*…*2*1

If you started with an **n** less than 1, you would never get a 1, so would, in a way, go off to +/- infinity.

If you wanted to have -9! = -362880, just rewrite it as -(9!).