Mark each statement True or False. Justify each answer.
(a) If sn → 0, then for every ε > 0 there exists N ∈ ℕ such that n ≥ N implies sn< ε.
(b) If for every ε > 0 there exists N ∈ ℕ such that n ≥ N implies sn< ε, then sn → 0.
(c) Given sequences (sn) and (an), if for some s ∈ ℝ, k > 0 and m ∈ ℕ we have |sn − s| ≤ k |an| for all n > m, then lim sn = s.
(d) and sn → s, and sn → t, then s = t.
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