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                                      Michael Lee's Mathematics and Physics

Why is the factorial of zero equal to one?  Intuitively, it would seem to be equal to zero but that is not the case.  Essentially, for this proof, if  0!  were to be equal to  0 then the factorial of one 1! must also be equal to zero which is absurd.  So if 0! is not equal to zero, then what is its value?

 

Brief reminder of what a factorial is as an example,  5!=(5)(4)(3)(2)(1) and so the factorial of five is equal to 5! = 120