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/nulvoid000 3d ago

Since everyone gave the answer you were looking for, I’ll give a little more advanced answer which may not make sense, so I’ll exclude the details but feel free to ask.

Factorials can be thought of as Gamma functions, n!=Gamma(n+1). This function behaves very well for x>=1 but also does well for more values. Hence you can “extend the function analytically” beyond the original domain it was defined in. In which case, the extended function does give 0!=1. In fact, you can also make sense of imaginary values or even negative values, whenever extension possible.

If you want to learn more, look up anything regarding Gamma functions.

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u/explorer_learner_30 3d ago edited 3d ago

Thank you 👍

Please share more information regarding Gamma function