Lost

Question

I can't understand this code
def is_even(x):
if x == 0:
return True
else:
return is_odd(x-1)

def is_odd(x):
return not is_even(x)

print(is_odd(1))
print(is_even(1))

why the result is different ! !

Answer 1

Let's see the function is_even(x). If x is 0, it returns true and otherwise returns is_odd(x-1), which returns not is_even(x-1).

For example, let's analyze is_even(4). First, 4 is not 0, so is_even(4) returns is_odd(3), which is not is_even(3). And is_even(3) returns not is_even(2). Then is_even(4) is equal to not not is_even(2), same with is_even(2).
Let's see 3 as example. is_even(3) is equal to not is_even(2), and is_even(2) is equal to not is_even(1). In other words, is_even(3) is is_even(1).

By mathematical induction, we can get that is_even(x) is is_even(x-2), and is_even(x) is not is_even(x-1), which is same with is_odd(x-1). So is_even(1) is is_even(3), and it is not is_even(2), and it is not is_odd(1). So is_even(1) is not is_odd(1).

Sorry for very long explanation..

Answer 2

is_even(4) is is_odd(3), which is not is_even(3).
is_even(3) is is_odd(2), which is not is_even(2).
Then not is_even(3) is not is_odd(2), which is not not is_even(2). So is_even(4) is not is_even(3), and not not is_even(2), which is same with is_even(2).

Answer 3

why is_even (4) equal ti not not is_even (2) ??! it should be equal to is_odd (2) and is_odd (2) returns not is_even (2)🤔

Answer 4

aaa now I understand so the key "not" is applied to both instructions of the fonction is_even "not is_even" returns false if x==0 and also (what I didn't notice ) it returns not is_od (x-1)

thank you very much