(Discrete math for computer science)

Hi I need help for solving this problem!! please solve this problem with kind explanation please!!

This homework is about representing things in terms of sets, and also with finding closed form expressions for summations.

Question : Let the set A be defined as follows.

A = { a | real(a) 0 a 1 }

That is, A is the set of real numbers between 0 and 1. Invent a way to represent the members of A using only sets. You are also allowed to use objects that were constructed from sets in the lectures, such as natural numbers and ordered pairs. You must be able to represent a real number with finitely many digits, such as 0.5, and a real number with infinitely many digits, such as 3. (These are only examples: you must be able to represent any real number in A.) Hint: think about summations.