poly_purple poly_purple - 1 year ago 109
Python Question

Understanding recursive odd/even functions

I'm currently studying python from http://www.sololearn.com/Play/Python and I'm having trouble understanding why this code works.

def is_even(x):
if x == 0:
return True

return is_odd(x-1)

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


I get how recursion works for a fibonacci and factorial but I can't wrap my head around this one.

Answer Source

is_even's base case resolves to True. Since is_odd(x) returns not is_even(x), the value True will be a part of the expression returned by is_odd. The question is how many times will that True value be negated. By tracing the calls you can see it will be negated an even number of times, and hence "retain" its truthiness, when x is odd [e.g.: x=3 ==> (not (not (not (not True)))) == True] and an odd number of times, and hence "lose" its truthiness, when x is even [e.g.: x=2 ==> (not (not (not True))) == False]. There's probably some term from logic that names this general property of multiple negation.

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