show that if sup = +infinity then there is a sequence of points sn in s such tha

Question

show that if sup = +infinity then there is a sequence of points sn in s such that sn converges to +infinity

(a) Let Si and S be two bounded, nonempty sets of real numbers. Prove that (b) Let S be the set consisting of all numbers of the form a + a2 where ai e Si and a e S2. Prove that aup(sup[S+up(Sa). such Show that if sup S = +00, then there is a sequence of points sn that s",-+ + o. a 0. Prove that . Let S be a set of real numbers and suppose that sup {az | z e S} = a sup s. Let {an)and be bounded sequences and define sets A, B, and C by A = {an), B = {bn), and C-(an+bn). Prove that sup C

Explanation / Answer

for every n in N(natural number) there exists s_n in S such that s_n > n (other wise n will be upper bound)

this is the required sequence

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