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

In mathematics, the factorial symbol is used to represent the product of all positive integers less than or equal to a given number. So, 5! = 12345 = 120.

The gamma function is an extension of the factorial function to negative numbers. It is defined as:

Γ(x) = (x-1)!

where x is a real number.

The gamma function is not defined for negative integers, because the product of all positive integers less than or equal to a negative integer is 0. For example, (-9)! = 012345678*9 = 0.

The gamma function can be used to calculate the factorial of any non-negative integer. For example, Γ(5) = 120.

Here is a table of some values of the gamma function:

x | Γ(x)

——- | ——–

1 | 1

2 | 1

3 | 2

4 | 6

5 | 24

6 | 120

…

As you can see, the gamma function is always positive for non-negative integers. This is why we cannot have negative factorials.