Using: [tex]x_n[/tex] −−−→ n→∞ L means ∀ε > 0 ∃N ∀n ≥ N |xn − L| < ε
Prove: If [tex]a_n[/tex] −−−→ n→∞ a and it has a sub-sequence [tex]a_n_k[/tex] with [tex]a_n_k[/tex] −−−→ k→∞ b then a = b.