![]() ![]() Now if I asked you how many arrangements there are of one thing you’d answer 1 because there is only one way to arrange one thing. (If you’ve ever studied sets, perhaps in basic statistics or discrete mathematics, you’re probably familiar with the concept of empty set. ![]() Zero factorial can be thought of as the number of arrangements of zero elements in a set, aka the empty set. Remember how we said that the factorial originated from the mathematical operation of finding the number of permutations or arrangements of a set? (Note: not the permutations of a smaller set from a larger set, but just the arrangements of a given set.) Zero factorial defined An Intuitive Understanding So what’s the deal? How did we decide that zero factorial equals one? It’s the mathematical equivalent to asking your parents why you have to follow some arbitrary rule they made up and being told, “because I said so.”Īlthough that might be an accepted parenting technique, it’s a lousy way to learn mathematics. Most people will tell you that 0! is defined as 1, and if you ask why they just say “because it’s defined as one”. the “product of all the positive integers less than or equal to the number” then figuring out 0! is like hitting a brick wall. This is where it gets tricky because if we only think of factorials in the context of which they’re usually defined, i.e. The factorial is sort of the unofficial operation of the multiplication rule of counting. The factorial was created as a way to express the number of arrangements of a group of items, which of course we find by using, in its most basic form, the multiplication rule of counting. ![]() You find factorials all over combinatorics because that’s where they originated. ![]()
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