SOLVED:Give the infimum and supremum of each unbounded set listed in Exercise 4.1.

SOLVED: Prove that a non-empty finite set S of real numbers has an infimum and a supremum and they are elements of S

SOLVED: Find the supremum nd the maximum, if they exist , of the function f(n)R defined by

SOLVED: Exercise 1.27: For each item, compute the requested supremum or infimum carefully. Explain why it does not exist. Either way, prove that your answer is correct.(a) Determine sup A for A = √n : n ∈ N.(b) Fix ε ∈ (0,1). Determine inf(B) for B = a^n : n ∈ N.(c) Fix a ∈ (1,∞). Determine sup(C) for C = a^n : n ∈ N.