That's what I meant by apples and oranges, I am arguing over the fundamentals because I am a purist, in isolation sqrt(x) has 2 values and that's why your paradox fails, you are arguing otherwise. xoolex gave the diplomatic answer, something we call sqrt(x) which has positive values only by agreement only.
Maths was developed by us, it is not a naturally occurring product, so those agreements are very relevant. Anyway, let's leave that argument aside as it seems settled. But I am not sure what failed paradox are you referring to?
Originally Posted by Crysthalica
Except 1/3 isn't possible to write in decimal, 0.33333~ is just the closest number possible.
Actually, I think that the multiplication is quite valid.
Also 0.999999... actually does equal 1. I proved it earlier