Can someone pleeeease explain this for me. Throughout all of my math classes, mostly Algebra, I was always told that zero factorial (0!) is equal to 1. Now I understand how 3! is the same as 6, and 5! is the same as 120, and so forth, but I cannot figure out the 0! mystery. Any help would be appreciated.
Don’t you think this should be in GQ?
(and sorry, can’t really help you with the math there)
Well, I really have no clue, but I’ve learned something about math. If it doens’t follow the rule then…theres a special rule!! or it is by definition :D. 0!=1 is probably the latter.
[Moderator Hat ON]
Yeah, I think this should go to the mathematically-inclined in General Questions. Here ya go, Manny, Nickrz…
[Moderator Hat OFF]
The most natural way is to think of it as an “empty product”. n! is defined to be the product of all positive integers less than or equal to n. That’s an empty set when n=0, so you’re multiplying over an empty product (there’s nothing left to be multiplied). Empty products are generally defined to be equal to 1, because that’s the multiplicative identity (the multiplicative “nothingness”, I guess you could say). Similarly, empty sums are generally defined to be 0, since that’s the additive identity.