I don't think I'm familiar with the rule you're talking about.
Nothing's off, our current application and notation for hexadecimal (and the word itself) just date back less than a hundred years. It was standardized in a culture where base 10 was already ubiquitous on a subliminal level; it's taught to people who have been counting in tens for their entire life.
This isn't an inherent trait of math in other words, it's an artifact of the anthropological context in which we're using that math. If we came from a long line of civilizations that defaulted to calculating things in base 16 (cause, I dunno, 4 fingers instead of 5), we'd have 16 unique digits and kids in school would get headaches remembering that you had to leave 6 of them out to do computer stuff in base 10.
Sure you have... we just call that one "thumb"
Yess, my point exactly. If " If we came from a long line of civilizations that defaulted to calculating things in base 16 (cause, I dunno, 4 fingers instead of 5), we'd have 16 unique digits" but we don't. I'm saying I think that's a manufacturing of this reality and I think to a certain extent everything else is based on that manufacturing.
In essence, it's interesting how there is nothing and , to my knowledge, there could never be anything oustide of 0-9 for us in terms of digits.
For example and to answer your question about the rule of 3. It's based on Nikola tesla's idea of the math vortex. Even using hexadecimal system, which I did slight research on since I had no knowledge on it, which is used to represent bits (binary digits " 0 and 1= 2 therefore binary) the cap you can reach is once again "9999". Even if ur in base 16, the limit at which the digits end even if being represented by a hexadecimal system is still... You guessed it "9".
The math vortex explains that any given number you take between 1 and 9 except for 369 you can take and double it or half it infinitely and the sum of that number will always be 1,2,4,5,7,8 and never be 369. I.E: 7x2=14... 1+4=5 ----- 14x2=28... 2+8=10.... 1+0=1 ------ However, with 369 the values will always and only be 369.
Basically, it somewhat explaines that 369 are sorta special or stand alone numbers. I'm not too sure because I'm still trying to understand it but 9 is definetly a cap on it no matter what. I mean even with your numerical system the binary cap will be 9999
And, for the roman numerals they have 7 base digits. Like your hexadecimal system. Which would refute everything I have said so far. However, as your hexadecimal system (and I took this from wikipedia so it's somehwat legitimate but not) "The largest number that can be represented in this manner is 3,999 (
MMMCMXCIX), but this is sufficient for the values for which Roman numerals are commonly used today, such as year numbers"....
Notice anything interesting about the digits.
M M M C M X C I X
1 2 3 4 5 6 7 8 9
That being a bit besides the point, no matter what number you'd ever want to make with roman numerals, it could never surpass (
MMMCMXCIX) 9 consecutive characters. It doesn't exist.