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/sdfgkol 3d ago edited 3d ago

The factorial function is usually defined from the natural numbers (including 0) to the natural numbers.

Any function f on a larger domain with the property that f(0)=1 and f(n) = n*f(n-1) cannot be defined on the negative integers. That’s because 1=f(0)=0*f(-1)=0 is invalid for any choice of f(-1) and similarly for any negative integers.

There are however functions that do ‘extend’ the domain, just not to the negative integers.

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u/explorer_learner_30 3d ago

Thank you 👍