We never
talk about
factorial of
negative number.
But why not?

\( -1! = ? \)

Long ago, I made
simple Basic language
program to calculate
factorial of number in math.

In math, the factorial of
a non-negative integer n,
denoted by \(n!\), is the 
product of all positive 
integers less than or equal to n

Oh, what is
factorial?

In other words,
$$n! = n \times (n-1) \times (n-2) \times \ldots \times 2 \times 1$$

\( n = -1 \)

But when I entered
\( n = -1 \)
by mistake, my code
couldn't stop and it
crashed as the answer
got so big number.

The concept of an
ever-increasing number
sparked an idea in my mind:
what if 

\( -1! = \infty \) ?

to \( \infty \)
and beyond

Also I remembered
this formular.

$$_nC_k=\binom{n}{k} = \frac{n!}{k!(n-k)!}$$

In math,
this is combination,
which refers
to a way of selecting
items from a group, 
where the order
does not matter.

Of course there's no way.
which means

\( _3C_4 = 0 \)

Yes, this must be 0.

$$_3C_4=\frac{3!}{3!(3-4)!}
= \frac{6}{6(-1)!}$$

Well,
factorial of negative
number was
never part of
math, but why not?

So it would
be pretty convenient
if we agree
$$ -1! = \infty $$
just like we did with
$$ 0! = 1 $$