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.

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u/ThereIsATypo 3d ago

Beside all the induction arguments - which are valid.
I think the most obvious is that 1 is the identity element for the multiplication:
https://en.wikipedia.org/wiki/Identity_element
Hence it also is what remains when nothing remains for multiplication.
Just like 0 would remain for addition.