Representing finite discrete space

Question

As far as I can tell, not being a mathematician, a finite state space, ranging from 1 to 3, can be represented by a simple A={1,2,3}, its notation being correct. A question then follows: - How to represent a discrete state space, with starts at element a, up until b, but, with an incremental value of c per element?

Answer 1

You could use set-builder notation and write something like $\{a+kc:k\in\mathbb N_0,a+kc\le b\}$. This depends on if you're comfortable with notation like $\in$, what you call the set of nonnegative integers, and whether this would really be better/clearer than something like "the sequence of values from $a$ to $b$ with increment $c$".