Let D(x) represent enjoyment as a function of x, where D(x) is a continuous function mapping R to R. The following properties are satisfied:
- Limit of enjoyment as activity increases indefinitely:
Enjoyment decreases and tends to vanish as the activity increases without bounds:
lim(x → infinity) D(x) = 0 - Bounded enjoyment:
There exists a positive constant C, such that for any x, enjoyment cannot exceed this value:
|D(x)| ≤ C, for all x in R. - Dependence on a personal values matrix:
Let M represent the matrix of personal values, then:
C = k * determinant(M),
where k is a positive proportionality constant. - Matrix M as a function of time and information:
The matrix M is defined as:
M = f(time, information),
where f maps the variables time and information to personal values.