6. The Time Scale Exponential

2. Definition of a Time Scale

A time scale is any closed subset of the real line.

Here are some examples of time scales.

These time scales are

• (a) The real numbers
• (b) Discrete time with spacing h.
• (c) The so-called quantum time scale.  Each point is a positive number q raised to an integer power.
• (d) The Log time scale.  The nth point is located at log(n+1).
• (d) The periodic time scale with period T.

Examples of subsets of the real line that are not time scales are the set of rational numbers, the set of irrational numbers, and the open set of points on the interval (0,1)

Here are the different classification of points on a time scale.

                (From Bohner and Peterson.)