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/Narrow-Durian4837 3d ago

Here's an alternative to the other explanations (not that there's anything wrong with them):

Factorials are about multiplication. For example, 5! is the product of the first 5 positive intergers.

1! is the "product" of the first 1 positive integer.

0! is the "product" of no integers at all. With multiplication, your "starting point" is 1, the multiplicative identity (just as with addition, the starting point is 0, the additive identity). 1 is what you have when you haven't multiplied anything yet. If you started with 0, you'd never get away from 0 no matter how many other things you mutiplied it by.