>>13733800You have to show that there exists an irrational number between 3 and 4 that can't be added in this system such that is has a unique name.
If its the case that ANY irational number can be added and it will have a unique name then that means all irrational numbers can be mapped to by this method.
The whole point is that we can uniquely represent any irational number between 3 and 4 using only a subset of "natrual" numbers.you would need to use the 101 tree for 3-4, you could then use 202, 303, 121,131, etc for all the other intervals.