I've not disputed any of this, I understand all of this completely, but a fractional representation of value is not a value. We use fractions as a 'rational numbers' in order to make mathematics function, just like we use 'complex numbers' and 'irrational numbers' to make mathematics work. That has nothing to do with my very simple and yet somehow evocative statement, that one can't be divided by three without a remainder. For some odd reason, that fact seems to blow your minds! You seem to think I am some sort of moron to believe that! But really.. there IS a remainder when you divide one by three. The same remainder as you have when you divide 10 by three, or 100 by three. The fact that you can't tell me how to evenly divide $100 between three friends, has nothing to do with not having the proper coin values, it's because there is a remainder when you divide 1 by three, in any base 10 math.
This has nothing to do with "thirds existing" or anything else, really. We assume the remainder, because the remainder is inconsequential, because we are never going to calculate to infinity. We don't need to resolve what to do with this remainder to make 1/3 work or 3 x 1/3 = 1. Still... the remainder DOES exist.
5,263... we can get to 6,000... I know we can!!