Why is the factorial of 0 equal to 1?

Question

Wouldn’t this also mean that 1!=0!, why is this true?

In: 383

Answer 1

The real answer is “because we say so”. We define the factorial however we want. The other answers are justifications as to why defining 0!=1 makes sense.

We could say that 0! is simply not defined (as are -1! and 0.5!, for instance). However, it would mean we would have to deal with many special cases. We would have to do things like f(n)= … if n = 0 and … otherwise.

It is way more useful to just define 0!=1 so the equations look cleaner.

Edit : changed convenient to useful, as u/peeja’s suggestion.