One of the axioms of addition is the existence of additive inverse elements, (-x), such that x + (-x) = 0. Subtraction is just a shorthand for using the additive inverse. If subtraction does not exist, then addition is broken.Addition and multiplication work nicely with it.
however reading this suggests there is no subtraction (and therefore no division)
The problem with inclusive-or is that it loses information. x or 1 = 1 tells us nothing about x, so we cannot have an inverse, x or 1 or (-1) = x. Addition has to be exclusive-or.
(By contrast, multiplication is allowed to lose information, as long as it only happens when multiplying by zero. Every other element has a multiplicative inverse, so we can implement division by multiplying that. We only have one non-zero element, and it is its own inverse.)
Statistics: Posted by jojopi — Thu Sep 12, 2024 10:17 pm
