Unformatted text preview: ∃ K ∈ N such that ∀ n ≥ K , x n ≤ x and xx n < ε . (d) x = sup n ∈ N x n or x = inf n ∈ N x n . (e) x = sup n ∈ N x n and x = inf n ∈ N x n . (f) ∀ K ∈ N ∃ ε > 0 such that ∀ n ≥ K ,  x nx  < ε . (g) ∀ ε > ∃ K ∈ N such that ∃ n ≥ K , x n ∈ V ε ( x ). (h) ∀ ε > ∃ K ∈ N such that xε < inf n ∈ N x n ≤ sup n ∈ N x n < x + ε . (i) ∃ ε > ∃ K ∈ N such that ∀ n ≥ K , x n ∈ V ε ( x )....
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 Spring '08
 JUNGE
 Math, Calculus, Xn

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