Suppose that the set A is defined like this: A = { a | real(a) ∧ 0 ≤ a ≤ 1 } So A is the infinite set of real numbers between 0 and 1 inclusive. Show a way to represent all the members of A using only sets. Your representation must work for real numbers with finitely many digits, like 0.5. It must also work for real numbers with infinitely many digits, like π − 3. Hint: you can also use objects from the lectures that can be represented as sets, such as natural numbers and ordered pairs.

Suppose that the set A is defined like this: A = { a | real(a) ∧ 0 ≤ a ≤ 1 } So A is the infinite set of real numbers between 0 and 1 inclusive. Show a way to represent all the members of A using only sets. Your representation must work for real numbers with finitely many digits, like 0.5. It must also work for real numbers with infinitely many digits, like π − 3. Hint: you can also use objects from the lectures that can be represented as sets, such as natural numbers and ordered pairs.