For any two real sequences {an} and {bn}, prove that Rudin’s Ex. 5 We assume that...

For any two real sequences {an} and {bn}, prove that Rudin’s Ex. 5 We assume that the right hand side is defined, that is, not of the form ∞ − ∞ or −∞ + ∞.

lim sup (an + bn) ≤ lim sup an + lim sup bn.

Proof If lim sup an = ∞ or lim sup bn = ∞, there is nothing to prove

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Colby Messinger answered 2 years ago

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For any two real sequences {an} and {bn}, prove that Rudin’s Ex. 5 We assume that...

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