Re: Grammar for roman numerals

Martin Ward wrote:


> Taking the most liberal interpretation of the rule "a smaller number
> placed before a larger numeral should be subtracted from it,
> instead of added to it", every string of numerals has a valid interpretation.
> For example, "IXM" is interpreted as as IX (9) subtraced from M (1000)
> to give 991.


That's my understanding as well. Nonetheless I'm not sure of the full
algorithm, with regards to the total sum.


What about "IXIM"? Intuitively this would be 990 (-(-I+X+I)+M), but it
might be calculated as (-I+X)+(-I+M) = 1008 as well.


Similarly: "IXX" vs. "XIX", where "IX" is a smaller number, and "XI" is
not a smaller number, than the following numeral "X".




> This method has the advantage of providing representations for zero
> and negative numbers: for example VVX is one representation of zero,
>
> If only the Romans had followed the Robustness Principle, they might
> have discovered zero and negative numbers, and changed the course
> of mathematical history!


Great ideas :-)


DoDi

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