>>333
>\[|\mathbb{R}| = |\mathbb{Z}|\]
I didn't really mean that real numbers are badly contructed, by mathematicians, but the world is more likely based on discrete numbers than on "real" numbers and the latter is a formal contruction where distance between numbers is "really infinitely" small. 

You seem to use axiom or principle that you can count from 0.1 to 0.(1). I won't probably disprove or confirm your theorem because it is not my focus in my journey through the land of mathematics. xp I only had thought that you can add from 1 to \[+\infty\] with it, but it's not limit of adding smaller values so they en up in a fixed value.