CABOOSE Readers...This is an immediate result from the assertion that subtraction and division are historical artifacts which arose in mathematical reasoning, but cloud the basic concepts of computation. They might be best called meta-operations. In terms of revamping computing theory so it is based upon ( +, *, -Z, 0, +Z ), one will see that ( +, * ) both associates and commutes in terms of ( -Z, 0, +Z ). And, it follows that they can distribute when used in conjunction. And, the simplistic tuple ( numerator, denominator ) used as a data structure of type ( [ +Z | -Z | 0 ] , [ +Z | -Z ] ) can represent (-Q, 0, +Q) when needed!So, with a slight gesticulation one might claim that additive and multiplicative inverses and identities exist for every element of the sets on which these operators work. So, talking hands say this whole contraption of cognition is somewhat group-ish and possibly Abelian. Needs be that this amateur mathematician brush up on his modern abstract algebra, but one nice feature of certain groups is that any combination of the available operators and members of the available numeric sets produce members within that set. And, one of the fundamental concepts from current computing theory is that every algorithm is ultimately integral number whose inputs and outputs are interpretable as integers and that is processed by a general-purpose algorithmic solver, also representable by an integer. So, in the infinite integral range of values, a number whose algorithmic interpretation maps between a desired input and a target output must exist! Finding it might be a challenge. This might be enhanced by a well-designed optimization problem where this algorithmic number is a global extremum. Yet, with a non-nonchalant wave of the hand, one can boldly claim that all "should be computable". Yet, the Bressler-Bischoff Theory of Human Socio-psychology says that some aspects of reasoning will never resolve themselves in a finite amount of time, such as, the purported equitable partitioning of an American quarter producing a dime and a nickel! This simply does not compute!
Please Keep IT Simple! The Future of Computing Undergirding An International Community Depends Upon IT!
