The Definition of a Zero Factorial This still counts as a way of arranging it, so by definition, a zero factorial is equal to one, just as 1! is equal to one because there is only a single possible arrangement of this data set. Simple “Proof” Why Zero Factorial is Equal to One
What it means is that you first start writing the whole number n then count down until you reach the whole number 1. For the equation to be true, we must force the value of zero factorial to equal 1, and no other. Otherwise, 1! ≠1 which is a contradiction. The value of 0! is 1, according to the convention for an empty product. The factorial operation is encountered in many areas of mathematics, notably in combinatorics, algebra, and mathematical analysis. Its most basic use counts the possible distinct sequences – the permutations – of n distinct objects: there are n!. Factorial, in mathematics, the product of all positive integers less than or equal to a given positive integer and denoted by that integer and an exclamation point. Thus, factorial seven is written 7!, meaning 1 × 2 × 3 × 4 × 5 × 6 × 7. Factorial zero is defined as equal to 1. Factorial. Quick Facts. Hope this helps!
