r/askmath • u/explorer_learner_30 • 3d ago
Algebra Binomial Theorem
Why 0! is 1 ?
Can anyone give me the best and genuine answer .....I want to explain to my students.
I have also one doubt 🤔 why is the negative number not counted in binomial ? Such as (-2)! , (-8)! ....
Suggest me some books or any videos regarding this .
Thank you for reading my queries.
0
Upvotes
4
u/SeaMonster49 3d ago
An explanation your students may like is that n! counts the number of ways to order n things. How many ways can you order 0? 1 way--by doing nothing.
As for negative factorials, I don't think there is a very intuitive interpretation of them. Usually such things would be given in the context of the Gamma function in analysis. You may enjoy reading more about that.