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

2! is what you get when you multiply 1 by 2.

1! is what you get when you multiply 1

0! is what you get when you multiply

So 0! is what you get when you’re multiplying, but you’re not putting anything in. That’s called the empty product. The empty product is usually defined as 1, because that’s the multiplicative identity- same as how the empty sum is 0, the additive identity. 1 is nothing in the context of multiplication, not 0.