It follows that a set A is bounded if and only if there exist M∈R such that |x|≤M for all x∈A (see Exercise 1.5.1) \(x \leq \alpha \text { for all } x \in A...It follows that a set A is bounded if and only if there exist M∈R such that |x|≤M for all x∈A (see Exercise 1.5.1) x≤α for all x∈A (that is, α is an upper bound of A); x≥β for all x∈A (that is, β is a lower bound of A); Prove that a subset A of R is bounded if and only if there is M∈R such that |x|≤M for all x∈A.