(6th-March-2020)
T is discrete if there exist only a finite number of time points between any two time points; for example, there is a time point every hundredth of a second, or every day, or there may be time points whenever interesting events occur. T is dense if there is always another time point between any two time points; this implies there must be infinitely many time points between any two points. Discrete time has the property that, for all times, except perhaps a last time, there is always a next time. Dense time does not have a "next time." Initially, we assume that time is discrete and goes on forever. Thus, for each time there is a next time. We write t+1 to be the next time after time t; it does not mean that the time points are equally spaced. Assume that T has a starting point, which we arbitrarily call 0.
Suppose Pis the set of all possible percepts. A percept trace, or percept stream, is a function from T into P. It specifies what is observed at each time.
Suppose Cis the set of all commands. A command trace is a function from T into C. It specifies the command for each time point.
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