Each domain represents a set of possible values, with X being the set of possible values upon which the function operates and Y the set of possible values that can be produced by the function. X is the domain of possible messages that might be transmitted and Y the domain of possible received messages, with the values in Y being the information about the process and set X . For example, a square root function may be defined as operating on any positive integer, while it may also be applied to specific number, e.g. 16.The particular value x is bound to X , taking a specific value. That is, the characteristic X has in a particular instance, the value x . Each function physically implements a channel , a causal mechanism that converts or transmits values from the initial domain X to domain Y .
System information is based on the relationships between the characteristics' values in the output.
The quantity of information is measured by counting the relationships or a surrogate for the relationships. As these relations are produced by functions or processes, and only by functions, we may claim that information is contained in and only in the values returned by a function. Given our definition, information is not the process itself. The input to the process is not information about the process, although it clearly may be information about another process.