Value of 0!

Factorial of a natural number n is defined as the product of all positive integers from 1 to n. Mathematically, n! = 1 x 2 x 3 x ... x n. For example, 5! = 1 x 2 x 3 x 4 x 5 = 120.

However, the factorial of 0 is a special case. By definition, 0! is the product of all positive integers from 1 to 0. But since there are no positive integers between 1 and 0, the product is empty. So, what is the value of 0!?

The answer is 1. While it may seem counterintuitive, the value of 0! is defined to be 1. This is because 0! is the empty product, and the empty product is defined to be 1. This convention is used to extend the factorial function to include 0 as a valid input.

In other words, 0! is not equal to 0, nor is it undefined. It is simply defined to be 1. This definition is consistent with the recursive definition of the factorial function, which states that n! = n x (n-1)! for all n greater than or equal to 1. This definition implies that 0! = 1, since there is no need to multiply by any positive integer between 1 and 0.

Therefore, the correct answer is option B: 1.