ABSTRACT
This chapter introduces basic algebraic inequalities used to prove the inequalities in the book as well as some basic properties of algebraic inequalities. A method for testing algebraic inequalities by Monte Carlo simulation is also introduced. Various classes of algebraic inequalities that permit natural meaningful interpretation are introduced as well as transformations of algebraic inequalities which make them interpretable. In this respect, the important class of algebraic inequalities based on single- and multi-variable sub- and super-additive functions are introduced together with the conditions for their meaningful interpretation. Inequalities based on single- and multi-variable sub-additive functions can be interpreted meaningfully if their variables and the separate terms in the inequalities represent additive quantities. The generated new knowledge can be used for optimising systems and processes in diverse areas of science and technology.
