NOT.Preface:4.1 - Construct the expressions and their interpretation

A group uses a simple rule, r(q,b) = q + q + b, over real numbers. Here q is one supplied input value and b is a shared parameter. The immediate work is to obtain values, inspect dependence on b and change that parameter. This stipulated mathematical example supplies its own interpretation; applying it to a price, measurement or other subject would require a separate account of that subject.

NOT.1 makes the operations explicit. A list of output values supports lookup at listed inputs. It does not necessarily support changing the rule or obtaining an answer at an unlisted input. NOT.2 fixes the references: both q occurrences use the same supplied value; b denotes the same parameter throughout this use. Parentheses or graph connections determine which operands each addition consumes.

For an operation graph, connect the input q to both inputs of one addition, then connect its result and b to a second addition. NOT.3 interprets those connections as addition of the supplied real values. With b=1 and q=0, 1 and 2, the outputs are 1, 3 and 5. A reader can obtain them by following the graph without a software implementation.

NOT.4 permits the transformation q + q + b to 2*q + b under that interpretation. The arithmetic identity supplies preservation for every admitted q and b. A shorter inscription may be useful for changing or explaining the rule, but its symbol count does not establish that every reader will find it easier.