Suppose I have a set of numbers. Then, suppose further that I take a sample of this set. Which of my sentences is correct? and why?
Let (0,2) be a sample from a set S of discrete numbers
Let (0,2) be a sample from set S of discrete numbers
The first is correct. When you are first introducing an unknown object in a discussion (in this case, some arbitrary set S of discrete numbers) you have to precede the noun with the indefinite article 'a' or 'an'. Using the indefinite article is not optional in English, in this case.
Another way you could say that is:
Let (0,2) be a sample from a set of discrete numbers, S.
Given a set of discrete numbers, S, let (0,2) be a sample from S.