Answer to Question #308427 in Real Analysis for Pankaj

Question

Let

(a↓n)↓n∈ N be any sequence. Show that Lim a↓n =L where n approaches ∞ iff for every ε >0 there exists

some N ∈ N such that n ≥ N implies a↓n ∈ N↓ε (L)