Final answer:
0 factorial, denoted as 0!, is equal to 1. This definition aligns with the combinatory interpretation of factorials and simplifies many mathematical expressions, including those in series expansions and the binomial theorem.
Step-by-step explanation:
The question is asking about the mathematical concept of factorials, specifically the factorial of zero (0!). In mathematics, the factorial of a non-negative integer is the product of all positive integers less than or equal to that number. The factorial of zero is defined as 1. This might seem unintuitive at first, but it is consistent with the combinatory interpretation of factorials. Whenever we select 0 items from a set, there is exactly one way to do so - select nothing. Thus, 0! is equal to 1. It's also consistent with the concept of the factorial function which maps the non-negative integers into the positive integers, and leads to a cleaner evaluation of many mathematic expressions including permutations, combinations, and series expansions, such as the binomial theorem.