Question

is (n-.5) factorial real? What i mean is, is that a legitimate thing? so that if n were 7, it would be 6.5! and would 6.5! be 6.5*5.5*4.5....?

Answer 1

There is a factorial of non-negative integers, but it's defined differently (the gamma function). So e.g. $6.5!$ is not equal $6.5\cdot5.5\cdot 4.5 \cdot\ldots$