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

Everyone here’s talking about combinatorics, which is a useful way to visualize it intuitively, but the real, mathematically rigorous reason has to do with the mathematical definition of the factorial, which doesn’t have to do with combinations (though that’s one useful application).

Definitionally, a factorial is a product of successive terms. The key is what is the empty product? What is yule product of the integers in the empty set?

The answer is 1, the empty product is 1, because the multiplicative identity is 1, just like the empty sum is 0, because the additive identity is 0.