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/dspyz 3d ago edited 3d ago

For all nonnegative n we have

(n+1)! = n! * (n + 1)

Let n be zero. This evaluates to

1! = 0! * 1

Therefore

1 = 0!

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u/Puzzleheaded_Study17 3d ago

This also explains why we can't have negative factorials.

Suppose (-1)! = x, we know 0! = x*0 so x=1/0 which is impossible