Ok now we're talking: important clarifications. Neat read on the type systems. But this part is extremely important:
> The idiomatic way to do it is to allow garbage inputs like negative numbers into your square root function, and return garbage outputs. It is in the theorems where one puts the non-negativity hypotheses.
The equivalent condition here would be for everyone to include "zero-ness" checks on their numeric inputs. But that's awful, because whereas everyone agrees that nullptr is a meaningless pointer, zero is in fact a perfectly good integer/float whatever. So now you have something worse than null pointers- which have course caused us a huge amount of pain ever since being inflicted on the world
So x / 0 = 0 is still a terrible, terrible, idea. But introduce something like the floating-point equivalent of NaN, and say x / 0 = NaN, and now your outputs will at least be obviously wrong, instead of just silently wrong
> The idiomatic way to do it is to allow garbage inputs like negative numbers into your square root function, and return garbage outputs. It is in the theorems where one puts the non-negativity hypotheses.
The equivalent condition here would be for everyone to include "zero-ness" checks on their numeric inputs. But that's awful, because whereas everyone agrees that nullptr is a meaningless pointer, zero is in fact a perfectly good integer/float whatever. So now you have something worse than null pointers- which have course caused us a huge amount of pain ever since being inflicted on the world
So x / 0 = 0 is still a terrible, terrible, idea. But introduce something like the floating-point equivalent of NaN, and say x / 0 = NaN, and now your outputs will at least be obviously wrong, instead of just silently wrong