The glib answer - it is needed for all of the math to work

The real answer - ooooookaaaayâŚ

My favorite way to think about factorial numbers in that `n!`

means âhow many different ways can I arrange `n`

balls of different colorsâ.

Suppose I have 3 balls, `['red', 'yellow', 'blue']`

.

There are `n! = 3 * 2 * 1 = 6`

ways for me to arrange these balls:

`['red', 'yellow', 'blue']`

`['red', 'blue', 'yellow']`

`['yellow', 'red', 'blue']`

`['yellow', 'blue', 'red']`

`['blue', 'red', 'yellow']`

`['blue', 'yellow', 'red']`

From this you can see, this ball arranging definition makes sense, because I have `3`

choices for my first ball. Once Iâve picked my first ball, I have `2`

choices for my second ball, and after that I have `1`

choice for my remaining ball. Thatâs a total of `6`

different ball arrangements.

This pattern works for any number of balls.

Now, how many different ways can you arrange `0`

balls?

âŚ

Exactly `1`

way! You do nothing, and that is the only possible arrangement.

Looking back at the glib answer now, this âball arranging logicâ shows up in a lot of deep mathematical logic, and this logic only works out right if we consistently use the idea that there is only `1`

way to arrange `0`

balls (or the equivalent statement for the various deep mathematical logic statements under consideration).