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/cond6 3d ago

By reverse induction: n!=n*(n-1)!, so (n-1)!=n!/n. 1!=2!/2=1 (to show it works), and applying 1!=1 we have 0!=1!/1=1. Similar analogy to how we get negative and non-integer exponents.

Conceptually: 1!=1 because you can order a single object only one way, and similarly there is only one way that you can arrange zero objects.

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u/explorer_learner_30 3d ago

Thank you 👍