For each of the following sets S, find sup(S) and inf(S) if they
exist:
(a) {x...
For each of the following sets S, find sup(S) and inf(S) if they
exist:
(a) {x ∈ R| x2 < 100}
(b) {-3/n | n is a counting number}
(c) {.9, .99, .999, .9999, .99999, …}
1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i)...
1. Consider the sequences defined as follows.(an)
=(12,13,23,14,24,34,15,25,35,45,16,26,36,46,56,17, . . .),(bn)
=(n2(−1)n)= (−1,4,−9,16, . . .).(i) For each sequence, give its lim
sup and its lim inf. Show your reasoning; definitions are not
required.(ii) For each sequence, determine its set of subsequential
limits. Proofs are not required.