Factorial Inequality Proof I need some help proving the following fact about factorials.
Let $a$ and $b$ be positive integers. Prove that if $a > b$, then $a! > b!$. 

If $a>b$ then $$a!=a \cdot (a-1) \cdot \ \dots \ \cdot (b+1) \cdot  b \cdot (b-1) \cdot \ \dots \ \cdot 1$$
so we would have
$$b!=\frac{a!}{a \cdot (a-1) \cdot \ \dots \ \cdot(b+1)} < a! \implies b! < a!.$$
