Question

how to prove that 0!=1

Answer 1

Hey friend, Harish here.

Here is your answer:

Mathematical Proof:

We know that.

  $(n)! = (n) (n-1)!$

⇒ $1! = (1) (1-1)!$

⇒ $(1-1)! = \frac{1!}{1}$

⇒ $0! = 1$

Hence proved.

Theoretical proof:

The factorial is a concept which is invented to find total number of possible arrangements easily.

For example:

 If we have 1 object and to arrange it in some manner the possible way is 1! = 1 way only is possible.

Suppose if we don't have a object, We can't arrange it in any manner which also become 1 possibility.

Hence 0! = 1

Proved.
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Hope my answer is helpful to you. : )