Question

What does "n!" mean?

Answer 1

`n!` is defined for all natiral numbers, `n in NN`, as the product of all natural numbers starting from 1 up to (and including) `n`.

`n! equiv 1 times 2 times... times n`

For convenience, we define `0!` to be 1.

Answer 2

If `n` is a natural number, then:

`n! =(n)(n-1)(n-2)...(1)`

For example,
`4! = 4*3*2*1=>24`

Interestingly, `0! =1`.

Why?

Hmm... let's wright down some factorials.

`5! =120`

`4! =24`

`3! = 6`

`2! =2`

`1! = 1`

Oh! we see that `5!` is five times larger than `4!`. Also, `4!` is four times larger than `3!` and so on.

Therefore, `1!` is one time larger than `0!`.

Therefore, `0! =1`

Of course, as you get advanced on functions, you will be able to calculate factorials of negative numbers, imaginary numbers, and so on. (These factorials will give mind blowing results!)