0! = 1 how?

We know that factorial of a number can be written as product of that number and factorial of its previous number. That is:

 n! = n × (n - 1)!

This can also be written as ratio of the given number’s factorial and the same number. It will be equal to factorial of its previous number as shown below:

 

n!n = (n - 1)!    

When the given number is taken as 1, it will be equal to its previous number’s factorial i.e. 0!.

For n = 1, so 1!1 = (1 - 1)! = 0!

Hence, 0! = 1.

 

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