1.(10 points.) Let the set A be defined as follows. 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 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 2. (10 points.) Let S(n) be the sum of the first odd natural numbers. For example: S(0) = 0-0 S(1) = 12= 1 S2) 22 1+3 93) = 3.1+3+5 S(4) = 4-1+3+5+7 Prove that S(n) = n2 for all natural numbers n. Do not use mathematical induction (even though it is possible to do so)