Fantastic. Addition in Doronetics is non-associative. That makes it inconsistent and useless.
Wrong. It is useful if C is local , for example:
(1a) 10 - 9.9 = (10*1) - (10*0.99)
(1b) (10*1) - (10*0.99) = 10 * (1 - 0.99)
(1c) 10 * (1 - 0.99) = 10 * (0.01)
(1d) 10 * (0.01) = 0.10
(2a) 10 - 9.9 = 10 - (9 + 0.9)
(2b) 10 - (9 + 0.9) = (10 - 9) - 0.9
(2c) (10 - 9) - 0.9 = 1 - 0.9
(2d) 1 - 0.9 = 0.10
It is not useful if C is non-local, for example:
jsfisher said:
(1a) 10 - 9.999... = (10*1) - (10*0.999...)
(1b) (10*1) - (10*0.999...) = 10 * (1 - 0.999...)
(1c) 10 * (1 - 0.999...) = 10 * (0.000...1)
(1d) 10 * (0.000...1) = 0.000...10
(2a) 10 - 9.999... = 10 - (9 + 0.999...)
(2b) 10 - (9 + 0.999...) = (10 - 9) - 0.999...
(2c) (10 - 9) - 0.999... = 1 - 0.999...
(2d) 1 - 0.999... = 0.000...1
Then again, Doron, you are just making this up as you go along. That's been made obvious by your shifting-sands arguments all along. First, (10 - 9..999...) is 0.000...1, but since that lead to a contradiction, you suddenly changed it. From that point forward, (10 - 9.999...) would be 0.000...10 (as if this extension to a meaningless notation lent to its meaningfulness).
jsfisher, your arithmetic is useless if non-local numbers are involved, as can be seen above.
... or finally just claim special rules apply.
Your associative property (ab)c = a(bc) is not a general rule, but you can't get it, jsfisher, because there is no such a thing like non-local numbers in your word (for example: 1=0.999...[base 10] in your word) so you can't get that A - (B + C) is not the same as (A - B) - C (the associative property (ab)c = a(bc) is not a general rule).
The non-associative property enables to refine arithmetic in order to deal with non-locality, which is something that your associative-only property can't do.
Furthermore, it is clearer now why you can't get non-locality (your arithmetic is associative-only, which is a direct result of your context-dependent only reasoning).
Your associative-only arithmetic is indeed "death by entropy" framework (you can't get that associative property is not a general rule, exactly as the second law of Thermodynamic is not a general law (it does not work among open systems).