Problem 2. [8 points] Let {an} be a sequence. Prove that {an} is convergent if and only if it satisfies the property that |an - m| < ε for all n, m ∈ N.
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This means that there exists a real number L such that for any positive real number ε, there exists a positive integer N such that for all n ≥ N, |an - L| < ε. Now, let's consider the property |an - m| < ε for all n, m ∈ N. We want to show that this property Show more…
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