Question

how can we prove that 0!=1?​

Answer 1

= 1 depends on your definition of "!". If your definition is n! is the product of the nonnegative integers less than or equal to n, while your definition of "product" incorporates the convention "an empty product equals 1" then the proof of 0!=1 is a two line proof applying the two lines of the definition, one by one.


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