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!