I had the function C wrong in my notes, which affected example #4 in the Alien math post. It should have been:
4. C(UU) = TRURTSUU…
I kept trying to calculate whether the functions in the sytem could represent all polynomials, all rationals, etc, and I kept coming up with results I knew were wrong. Eventually I realized it was function C which I had set up incorrectly.
#6 is still the same, because its the identity I thought the original C held for, but in fact it was wrong for that C and right for the correct C.
I also realized my numeral system was incapable of representing negative numbers directly, but it can do so using one of the functions.
This system was motivated by the same time of extensions that were used with our ordinary arithmatic, except that the start operator is different so the extensions are different, but they have parallels.
One of the functions / operators is a simple named one in our system. It was carried over because it fit naturally into the system. One of the other operators is named in some sources, but it is somewhat obscure. The rest are expressions, not fundamental functions or operators in our system.
This system makes some limited sense, as far as aliens using it. Certain expressions are a lot simpler in it, but derivatives and other calculations produce very messy expressions in the Alien system. Maybe parts of it are actually used with different names and symbols, in the real world.
I’ll reveal the big clue next week and then a couple days after that show the functions and operators.