Why 0!=1 Plz help me to prove this statement.
n! = n(n-1)!
1! = 1
so, 1 = 1*0!
thanks
To prove that 0! (0 factorial) is equal to 1, we can define factorials and use the fundamental properties of factorials.
Factorial is defined as the product of all positive integers less than or equal to a given number. For example, 5! is equal to 5 * 4 * 3 * 2 * 1, which is 120.
Now, let's consider 0! (zero factorial). By the definition of factorial, 0! should be the product of all positive integers less than or equal to 0. However, there are no positive integers less than 0. In other words, there are no integers to multiply together.
To handle this situation, we need to use the concept of the empty product. The empty product is defined as 1, which means that when there are no numbers to multiply, the result is 1.
So, even though there are no positive integers less than or equal to 0, we consider 0! to be the empty product, which is also equal to 1. Therefore, we can conclude that 0! is equal to 1.
In summary, 0! (zero factorial) is equal to 1 because it follows the definition of factorial and the concept of the empty product.