An Axiomatic Theory of Functions and Fluents

Publisher Summary This chapter discusses the theory of some basic applications of mathematics to science. It describes the concepts of pure mathematics such as the logarithm, the second power, and the product with substitutions in the area of those functions. The chapter examines scientific material such as time, gas pressure, coordinates, and objects that Newton called fluents. Furthermore, the chapter formulates articulate rules for the interrelation of fluents by functions. A function can be defined as a class of consistent ordered pairs of real numbers. Two ordered pairs of any kind are called consistent if their first members are equal while their second members are unequal. The empty function includes no pair. It is also noted that the intersection of any two functions is also a function.