In your "inverse implication" operator rationale, you say 0^0 is equal to 1.
That's not what I've learned. It's actually an undefined symbol:
https://www.wolframalpha.com/input/?i=0%5E0
(like 0 * Inf) and so on. So for floats this would be NaN.
Given that ints can't represent NaN it was probably proper to return something, in this case the limit value. But saying that the value of 0^0 is actually 1 is like saying 0 / 0 == 1 - it's also the lim(n->0), but for that Python actually returns:
Python 3.7.3 (default, Mar 27 2019, 22:11:17)
[GCC 7.3.0] :: Anaconda, Inc. on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> 0 / 0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: division by zero
>>> 0 // 0
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
ZeroDivisionError: integer division or modulo by zero
In your "inverse implication" operator rationale, you say 0^0 is equal to 1. That's not what I've learned. It's actually an undefined symbol: https://www.wolframalpha.com/input/?i=0%5E0 (like 0 * Inf) and so on. So for
floats this would be NaN.However, 1 is the limit of n^n as n->0: https://www.wolframalpha.com/input/?i=lim+n%5En+as+n-%3E0
Given that
ints can't represent NaN it was probably proper to return something, in this case the limit value. But saying that the value of 0^0 is actually 1 is like saying0 / 0 == 1- it's also the lim(n->0), but for that Python actually returns: