The factorial of a non-negative integer $n$, denoted as $n!$, is the product of all positive integers less than or equal to $n$. It can be defined as:

$n! = n \times (n-1) \times (n-2) \times \dots \times 1$

For example:

• $0! = 1$ (by definition)
• $1! = 1$
• $2! = 2 \times 1 = 2$
• $3! = 3 \times 2 \times 1 = 6$
• $4! = 4 \times 3 \times 2 \times 1 = 24$

Factorial is widely used in permutations, combinations, and other areas of mathematics involving discrete structures.

Do you want any further details or have specific questions?

Here are 5 questions to expand on this topic:

1. What is the factorial of 5?
2. How is factorial used in combinatorics?
3. Can you explain the relationship between factorials and permutations?
4. How do you calculate $n!$ for very large values of $n$?
5. How is the factorial function related to the gamma function?

Tip: The factorial grows extremely fast, making it useful for counting the number of ways to arrange or select items.