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is bigger than or equal for the Restrict inferior; if you will find only finitely many x n displaystyle x_ n wouldn't be regarded as convergence.) Since the Restrict inferior is at most the Restrict exceptional, the following disorders maintain lim inf n → ∞ x n = ∞ implies lim n → ∞ x n = ∞ , lim sup n → ∞ x n = − ∞ i
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Analogously, the limit inferior satisfies superadditivity: lim inf n → ∞ ( a n + b n ) ≥ lim inf n → ∞ a n + lim inf n → ∞ b n .The infimum/inferior/inner Restrict is often a set exactly where these accumulation sets meet up with. That is, it is the intersection of all the accumulation sets.under which a sequence of factors (