Semiotic Modeling for De-DuplicationJ.B. Phillips, R.Wiltshire, P.Prueitt, G.Price Engineering Development Institute and Highland Technologies Introduction and the commutative (otherwise referred to as the symmetric) property of equality (Kuratowski and Mostowski, 1968) states that if then However, these properties assume an altogether different meaning if A or B can change over time. Thus, if then the entire concept of equality is eroded substantially. Similarly, the concept of a function hinges on the constancy of values. If which is part of the definition of a function, contingent upon Eq. (4), then the concept of a function also assumes a dramatically different meaning. Moreover, assume that Then if it can be concluded that f is not a true function. Let X and Y be non-void sets. A function f from X into Y is a subset of X Y = {(x, y): x X, y Y} x X a unique y Y (x, y) f. The set X is called the domain of f, and we say that f is defined on X. The set {y Y: (x, y) f for some x X} is called the range of f, and is denoted by (f). (x, y) f, we call y the value of f at x and denote it by f(x). We write f:XY to denote the function f from X into Y, or mapping X into Y. |