14. Suppose that lim s,-s, with s>0. Prove that there exists Ne N such that s,>0 for all n≥N.

Suppose poset (A, R), where A = {1, 2, 3, 4, 6, 8. 9. 12, 16, 18, 32, 36} and the relation R runs outdivide. Answer the following questions:a. Draw a Hasse Diagram for the poset (A, R)b. Find the upper limit of {6, 9}c. Supremum of {6, 9}

Evaluate the limit 16 — а lim a → 16 4 – va uoation

b) Show that limn- n = x ≥ 0 if there is NE N, such that, for k2 N, k ≥ 0. Please follow steps below. Use the argument by contradiction: • Suppose that there is NE N, such that, for k≥ N, ak 20 and n = x < 0. lim 818