< A numbering system's basic requirement would be to be able to distinguish beetween the 'presence' and 'absence' of the physical entity being counted.>
That is very rational, however western civlization took a while to accept the zero.
Taken from the cover of book of Charles Seife "ZERO"
< The Babilonian invented, the Greeks banned it, the Hindus worshipped it,and the Christian Church used it to fend off heretic. Today it's a timebomb in the heart od astrophysics.>
I suggest check link related to unary numeration system.
Sorry I cannot help you, as engineer or naval architect my knowledge in theoretical math is very limited.