Hint: Consider xn = (xn + Yn) — Yn. - Let (xn) and (yn) be bounded sequences in R. Show that lim inf (x + yn) ≤ lim inf x + lim sup yn. 818 818 N→X

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.3: Algebraic Expressions
Problem 8E
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please help proof this and be specific so i can undersatnd. also please include the theorem that you are using to solve this too please

Hint: Consider xn = (xn + Yn) — Yn.
-
Transcribed Image Text:Hint: Consider xn = (xn + Yn) — Yn. -
Let (xn) and (yn) be bounded sequences in R. Show that
lim inf (x + yn) ≤ lim inf x + lim sup yn.
818
818
N→X
Transcribed Image Text:Let (xn) and (yn) be bounded sequences in R. Show that lim inf (x + yn) ≤ lim inf x + lim sup yn. 818 818 N→X
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