MATH.Preface:10 - Relations to further reasoning and work

FPF B.5.RC and B.5.RA recover an available construction or argument; B.5.RR follows a changed premise through it. Mathematical Thinking supplies specific constructions that such reasoning can recover, use and revise. B.5.QD develops a further question from an obstruction or a successful result; C.39.RO and C.40.CD support reusable operations and their development. A construction can be worth retaining because it makes another operation or question possible before its final application is known. When choosing which question to pursue, state the work its answer could enable; E.10.INT distinguishes that usefulness from other senses of interest.

For expressions, A.6.3.RT and A.6.3.RT.OE help make an operation performable in a notation. Mathematical Thinking constructs selected mathematical structures and transports their operations. Developing a notation for a new range of work can require additional notational-engineering methods.

For application, the C.29 family and B.5.MPC connect mathematical results, computational constructions and physical accounts. Method Engineering contributes when the result is used to design or revise a way of working. Other subject frameworks supply the physical, organizational or professional methods used with the mathematics.

For evaluating alternatives, reuse FPF’s characteristic, comparison and improvement methods. C.11 supports a consequential choice; C.11.DUA helps decide whether further calculation or inquiry can change that choice enough to justify its cost. Mathematical Thinking supplies the relevant construction or quantitative relation.