`text(Notation of factorial & its Algebra :)`

The continued product of first `n`, natural number is called as `text(n factorial)` and denoted by `n!` .

`n! =1 - 2 - 3 - 4 - ...... (n - 1 ).n!`

`4! = 4 - 3 - 2 - 1= 24`

`3! = 1-2-3 = 6`

`5! = 120; quad quad quad 6! = 720quad ; quad quad quad quad 7! = 5040.`

`text(Special Results :)`

`(A)quad quad``0! = 1` i.e. factorial of zero is `1`

`text(Proof:) quad n ! = (n - 1)! -n`

Putting `n = 1`

`1! = ( 1- 1)!.1 => 0! = 1`

`(B)quad quad` `text(Factorial of negative number is undefined)`

`(n-1)! =(n!)/n` if `n=0` then `(-1)!=(0!)/0=1/0 ` Not defined