State if the statement is true or false
Let (bn) be a sequence and B = {bn | n ∈ N} be the set of terms of the sequence (bn). State whether the following statements are TRUE or FALSE. If TRUE provide a proof and if FALSE provide a counter example.
(1) If (bn) diverges, then B is unbounded.
(2) If lim bn = b, then either sup(B) = b or inf(B) = b.
(3) If bn ≤ bn+1 for all n ∈ N and lim bn = b, then sup(B) = b.
