Formula for factorials, don't get it

Question

Hi if you look below, here's some code for calculating a factorial.
Ie. the factorial of 5 is 5! = 5*4*3*2*1
the factorial of 0 is 0!=1
After going round in circles I picked the code below off the internet.
But I am having difficulty with it.
The code creates a function called factorial and in its definition calls on itself
It's a recursive process I know... but how can a function be defined by itself?
Anyone can explain?
Thanks!
____________

"""Here we are setting up a prompt to ask for number going in"""
number=int(input("The factorial for "))
""" This is creating a function based on variable i"""
def factorial(i):
if i==0:
return 1
else:
return i * factorial(i-1)
print ( number, "is", factorial(number))

Answer 1

The function isn't defined by itself, but it keeps calling itself with the argument i-1 until the break condition (i==0) is True.

If you call factorial(5), the function will return 5 * factorial(4). So now the function needs to call itself again because it has no idea what factorial(4) is. And it learns that factorial(4) is 4 * factorial(3), so now the temporary result is 5 * (4 * factorial(3)). The function still has no idea what factorial(3) is, so it calls itself again with the argument 3 and the result is now 5 * (4 * (3 * factorial(2))). The function calls itself again: 5 * (4 * (3 * (2 * factorial(1)))). And again: 5 * (4 * (3 * (2 * (1 * factorial(0))))). Now, factorial(0) is called and that is the break condition. The function knows that when i == 0, it can stop calling itself and just return the result * 1. So factorial(5) is 5 * (4 * (3 * (2 * (1 * 1)))).

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