Part 2/5:
Another crucial aspect of factorials is the definition of 0!. By convention, the factorial of zero is defined to be 1. This is based on the principle known as the empty product rule, which states that the product of no numbers at all is 1. This definition proves useful in various mathematical scenarios.
Recursive Definition of Factorials
Factorials can be expressed through a recursive definition that connects the factorial of a number to the factorial of smaller numbers. The recursive definition states:
If
n = 0, thenn! = 1If
n > 0, thenn! = n × (n-1)!
This means that to calculate the factorial of n, one must calculate the factorial of n - 1 first.
For instance, to calculate 3!:
3! = 3 × (2!)And
2! = 2 × (1!)