MATH2400 Limits and Continuity Recall that limn→∞xn=L if ∀ϵ>0,∃M\stn>M⟹∣xn−x∣<ϵ. Proposition A converged sequence is bounded. Proof Suppose limn→∞xn=x Take ϵ=1. By definition, ∃M such that if n>M then ∣xn−x∣<1