User:Rudyeeeeeeee/Expanded Factorial Notation

Level 1: Factorial
In mathematics, the factorial of a non-negative integer $n$, denoted by $n!$, is the product of all positive integers less than or equal to $n$. The factorial of $n$ also equals the product of $$n $$ with the next smaller factorial:$$ \begin{align} n! &= n \times  (n-1)  \times (n-2)  \times  (n-3) \times \cdots \times  3 \times  2 \times  1 \\ &= n\times(n-1)!\\ \end{align}$$For example,$$\begin{align} 5! &= 5\times 4!=5\times 24=120 \\ & \quad\qquad = 4 \times 3!=4\times 6=24 \\ & \quad\qquad\quad\qquad = 3 \times 2=6 \end{align} $$The value of 0! is 1, according to the convention for an empty product.