A number system can be constructed based on 'rotators' rather
than the more common 'ordinals' that we are currently in vogue of
using.
The ordinals propagate carry/borrow between their respective
position as the number-line is traversed.
A rotator system keeps all carry/borrow activity confined within
the single 'digit'. Common mechanisms such as
addition/subtraction and multiplication are preserved. An outcome
of this application is that all operations are confined to the
single 'digit'. A numbering system based on the 'digits' (
modulos ) of the prime number set would look like this for the
first few numbers ...
Division is supported through multiplication with the 'inverse'
multiplier which can be obtained by inspection for any given
number. The inverse multiplier is that number when multiplied
with its generating number yields the result of 1: 11111. To find
the inverse multiplier for a number, just find the number that
when multiplied and all carries discarded within the 'digit'
modulo yields the result of one on each digit.
A rotator numbering system has a property similar to that of
'pure tones' that only interact between themselves, i.e.
orthogonal.
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